Homologous recombination is a type of genetic recombination that occurs during meiosis (the formation of egg and sperm cells). Paired chromosomes from the male and female parent align so that similar DNA sequences from the paired chromosomes cross over each other. Crossing over results in a shuffling of genetic material and is an important cause of the genetic variation seen among offspring.
Have you ever wondered why, when you look at a large family that has maybe 10 children, they all look related one to another? That is, you could all pick out that they were all members of the Brewster family, but yet it's pretty easy to distinguish one child from another. They look similar, but they also look different. And the reason for that is the term "homologous recombination". This is a type of genetic recombination that occurs during the formation of the egg and the sperm cells, and you'll recall formation of egg and sperm cells is called meiosis. During meiosis, what happens is that paired chromosomes from the male and the female parent align so that similar DNA sequences from the paired chromosomes have an opportunity to flip-flop, or to cross over one another. That crossing over results in the shuffling of genetic material, much as the very gentle shuffling of a deck of cards would do. And it's important because it's one of the sources of genetic variation that we see among offspring of parents.