Question

What does crossing over achieve for every specie in which it occurs?

Answer 1

It increases diversity in offspring. Kind of like rolling a die for some traits. Happens semi-randomly, but genes that are farther apart have a greater chance of crossing over.

Answer 2

Crossing over is a complex subject, but I will try my best to help you.
Crossing over is when two c'somes switch their genes around let's say these are c'somes: (the line is a separation of the two because Answers doesn't let there be a space between them.)

A l a
B l b
C l c
D l d

When crossing over occurs, the c'somes will cross and the genes will be exchanged from one c'some to another. The result may look like this:

A l a
b l B
c l C
D l d

Now, crossing over causes more diversity because this is how the genes get switched and this causes variation within the species. Variation causes genetic and biological diversity because if every organism would be the same for ever, with no change in DNA or mutations, then there would be no evolution, and the species would die out some time. Thanks to this, (crossing over and variation) evolution is possible, and there are differences between organisms of the same species.
I hope that answers your question!