I am studying recombination in Meiosis and the idea of crossing over doesn't make sense. My understanding is that 46 chromosomes in our germ-cell (23 from mom + 23 from dad) line up next to each other and recombine (swap areas of DNA). My confusion is that, since, for example, Chromosome 1 from mom is same as Chromosome 1 from dad, how is swapping areas of DNA going to exchange any information. Brown eye gene from dad would just be swapped with brown eye gene from mom. How will have any affect on the offspring? OR is it that if mom has brown eyes, the brown eye color gene in mom has something attached to it? OR is my understanding of genes incorrect and not every nucleus has all possible genes? (except the difference of X and Y chromosome.)?
There is quite a few misunderstanding in your question. So, I'll shortly give you some (simplified) definitions and then point you to another post.
Definitions and Basic Concepts
Now at any locus, you might see different individuals having different variants. For example an individual may have the sequence
ATTCT while another individual may have the sequence
ATTGT. Those different variants are called alleles. It is key to understand that there is genetic variation in populations. This genetic variation is a big part of the reason why people around you look different and why you ressemble more your siblings (if you have any) than a random person in the population.
How does recombination have any impact?
To understand the effect of recombination you necessarily have to picture a several loci model. As you now understand the above definitions you will find your answer at this post: Why do we need two markers to measure a recombination rate?
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