I will talk about humans only and I will not talk about the special case of sexual chromosomes (and anomalies such as trisomy 21) from the answer just to keep things easy. There is a lot to say, so I am just making a very short overview of different subjects. Get some coffee first, read slowly and don't hesitate to click on the wikipedia links to further your knowledge.
Pairs of chromosomes
We all have 46 chromosomes. The chromosomes can be arranged in 23 pairs. By definition the 3rd pair of chromosomes is the 3rd longest pair of chromosomes as you can see on this karyotype
You'll note that the 23rd pair is the pair of sexual chromosomes but I won't talk about them. Note by the way that species that have chromosomes present in pairs are called diploid. Some species are haploids (not pairs), some are tetraploids (4 chromosomes of the same type together), etc... While the terms "diploids species" is often used to refer to mammals for example, it is actually more correct to talk diplontic species. Diplontic species, are those species who are diploid most of the time and haploid only for a short period. Our ovules and spermatozoids are indeed haploids.
Pairs of chromatids
Chromosome are more-or-less X-shaped. Each "vertical line" of the
X is a double stranded (double helix) chromatids. Two chromatids of the same chromosome are called sister chromatids. Two chromosomes of the same pair are called homologous chromosomes. Note that chromosomes don't always look as they are represented here, it depends on the phase during the life cycle of the cell but this is a story for another time. As you said, one chromatid is made of two strands that are "anti-parallel". The point of the junction in the center (although it is note always in the center as you can see) of the X-shape is called the centromere.
In a pair of chromosomes, one chromosome is inherited by the father, the other one by the mother. Therefore we receive exactly the same amount of genetic information from each parent (but see this post). The egg actually receive 2 single chromatids (one from the ovule and one from the spermatozoid). At some stage of the life cycle each chromatid duplicate to make those X-shaped chromosomes. Therefore, two sister chromatids are exactly (except exceptions!) identical. However, because one chromosome come from the father and the other one from the mother, two homologous chromosomes are not exactly identical. Note that mutations occur during replication of DNA (especially during meiosis). Note also that at the moment of producing our gametes (=spermatozoids and ovules), chromatids from different chromosomes (within the same pair) can exchange DNA. This process is called crossing-over. Here is a schema of this process
Crossover is the process by which two chromatids from different homologous chromosomes exchange their DNA. Chromatids do not merge into one (as suggested in your below comment). Look at the above picture. Top left are the two homologous chromosomes. Top right are the two homologous chromosomes after crossover (a little pink piece is now attached to a blue chromatid and vice-versa). In the bottom are the four resulting gametes (the 4 independent chromatids) after meiosis.
While crossover refers to the mechanism, recombination refers to the statistical association between two loci. On the above picture there are two loci represented and both are heterozygotes (see below for definition) as at one locus are the alleles
aA and at the other locus are the alleles
bB. Of course, on the sister chromatids both alleles are the same given that the two chromatids are just copy of one another where one comes from one parent. Therefore,
a is always with
A is always with
B on the same chromatids. In the absence of crossover, we say that they segregate non-independently. If the offspring get
A, (s)he will necessarily get
B as well. However, if crossover can occur in between the two loci, then some gametes can carry
B and some others can carry
b. The statistical association between two locus is referred to as recombination. the recombination rate between two loci indicates the rate with which a crossover will occur between these two loci.
When talking about DNA, we usually refer to one double helix (one chromatid). DNA, is made of different chemical compounds including the nucleotides. There are 4 types of nucleotides that we are reffering to by the first letter of their names, A, T, C and G. Every time there's a T on one strand there is a A, in the other strand (and vice-versa). Every time there's a G on one strand there is a C, in the other strand (and vice-versa). In consequence one strand is some kind of a negative (photography) of the other strand.
From gene to protein
You can refer to a position on a chromosome as a locus. At different loci are different types of sequences. Without going into the details, a gene is a type of sequence that is used to make a protein. In order to make a protein from a gene, the double helix has to open up over a short region, some proteins come, read the DNA and make up an RNA out of it. The RNA is some kind of negative of the DNA strand that has been read (except that the Ts are replaced by Us). From the RNA some other mechanism (ribosomes; ribosomes are actually made of other RNAs but this is also a story for another time) make a protein our of the RNA. Here is an extremely simplified schema of this process.
Effects of the genotype on the phenotype
As I said above, there are some differences between homologous chromosomes. Consider for example that in a population, at a given locus (let's assume this locus correspond to a gene for simplicity) different chromosomes carry different variants. These variants are called alleles. The words recessivity, additivity or dominance refer to the relationship between two different alleles at the same locus in terms of how the two alleles affect the phenotype. Referring from wikipedia
A phenotype [..] is the composite of an organism's observable characteristics or traits, such as its morphology, development, biochemical or physiological properties, phenology, behavior [..].
Recessivity, additivity and dominance
Let's call one allele
Aand the other allele
a. Given that one individual has two chromosomes, this individual at the locus under consideration can be either
AA. The difference between
Aa is that in one case the
A allele comes from the mother while in the other case it comes from the father. It essentially makes no difference, so let's just call these two types
A are said additive if the phenotype
aA is the average phenotypes between the phenotype of
AA. If the phenotype
aA is closer to the phenotype
AA than tow the phenotype
A is said to be partially dominant and
a is partially recessive (or vice-verse for the opposite scenario). In the extreme case where the phenotype of
aA is exactly like the phenotype of
A is said to be dominant and
a is recessive (or vice-verse for the opposite scenario). Overdominance is a third type of relationship where the phenotype of
aA lies outside the range of phenotypes of
AA. Such as for example individuals having both
AA genotypes are small while individuals being
aA are big. Btw,
aa individuals are said to be homozygous while
aA are said to be heterozygous regardless of the functional relationship between the two alleles.
Consider for example a disease that is expressed only in the
aa genotypes. In such case
a is recessive. If two
AA individuals mate together there is no risque for the child to carry the disease. If one
aA individuals mate with a
AA individual the child is either
aA (with probability 0.5) or
AA (with probability 0.5). If two
aA mate together, than a child is
aA (with probability 0.5),
AA (with probability 0.25) or
aa (with probability 0.25). In other words, if two heterozygotes individuals mate together, they have a probability 0.25 that a given child will carry the disease if the disease is recessive. This probability reaches 0.75 if the disease is dominant (but the two heterozygote parents would both express the disease as well).