Humans have 2 copies of each chromosome, except for the sex chromosomes where females have X and X, but males have X and Y. When sex cells, which have one copy of each chromosome, combine they create an embryo that will become many body cells later. If meiosis didn’t create half the amount of DNA of body cells, than sex cells would have 2 copies of each chromosome and the embryo would have 4 copies of each chromosome. Then the next generation embryo would have 8 copies, then 16 copies, and so on. So to keep the number of chromosomes from not doubling each time, it’s important for sex cells to have half the number of chromosomes as body cells. This way, when two sex cells combine, they create a body cell with the right number of chromosomes.

Well, in plants, meiosis makes spores, not sex cells, but the process is the same.

If you didn't have half the DNA, then fuse the cells together to make a zygote, you would wind up doubling the amount of DNA in a cell with every generation. Pretty soon the cell wouldn't be able to hold all of the DNA it would be building up, and you would be sterile.