Refer to the following image. What you want to note is that this is a mitotic chromosome. Your cells are generally diploid, meaning for humans where n=23 your somatic cells have 46 chromosomes that form 23 homologous chromosome pairs.
For each chromosome in a pair, they have what amounts to the same genetic information with variations. At the locus for hair color, it will always code for the color of your hair but since you got half your genetic information from each parent, on one homolog the hair color locus might amount to red hair, while the other one might amount to brown hair. Scroll past the image:
In summary, the gene locus is for hair color, but there are red and brown alleles, or variations in a given gene locus for a given trait (see gene mapping). Thinking about traits and how they translate to features is complex in humans however due to features of our genomes such as epigenetics, epistasis, pleiotropy, etc. So when we describe in genetics traits such as color and how those related to AA, Aa or aa and so forth, it's nice to look at a much more simple organism like the pea plant that Mendel studied.
As for which allele is dominant? The actual wikipedia page for genetic dominance provides a good section:
By definition, the terms dominant and recessive refer to the genotypic interaction of alleles in producing the phenotype of the heterozygote. The key concept is genetic: Which of the two alleles present in the heterozygote is expressed, such that the organism is phenotypically identical to one of the two homozygotes. It is sometimes convenient to talk about the trait corresponding to the dominant allele as the dominant trait, and the trait corresponding to the hidden allele as the recessive trait. However, this can easily lead to confusion in understanding the concept as phenotypic. For example, to say that "green peas" dominate "yellow peas" confuses inherited genotypes and expressed phenotypes, and will subsequently confuse discussion of the molecular basis of the phenotypic difference.
Good place to start: Wikipedia
What you should also note is that dominance isn't intrinsic to the allele. Just because it's dominant to another allele doesn't mean it can't be co-dominant with another, and so forth. It also has no bearing on the population distribution of alleles, as certain dominant or recessive alleles can be either exceedingly rare or excessively common.