Why is it necessary for chromosome number to be halved during meiosis?

Meiosis reduces the chromosome number from diploid (2n) to haploid (n).  All human somatic cells have a diploid chromosome number of 46, whereas the human gametes (sperm and ova) have a haploid chromosome number of 23.  During fertilization, a haploid sperm cell and a haploid egg cell combine to form a diploid zygote.  Each parent contributes 23 chromosomes to the offspring so that it has a total of 46 chromosomes.  Hence, meiosis halves the chromosome number, but the diploid condition is restored during fertilization.  If meiosis did not occur, the chromosome number would continue to double with each successive fertilization.   In the absence of meiosis, a mating between two individuals with a diploid number of 46 would result in offspring with 92 chromosomes!  Each species has a characteristic chromosome number, and meiosis ensures that this chromosome number is maintained.

Well think about it... We have 23 pairs of chromosomes, half from our mother and from our father.  Meiosis is the bodies way of making sex cells or gametes.  The easiest example is when we look at a male.  The first thing a cell does is to duplicate it DNA, so the cell starts out with 46 pairs of chromosomes.  So this cell has a bunch of sister chromatids, and if you know mitosis, goes through prophase, metaphase, and telophase.  All this to segregate to two new cells.  During metaphase, the process of crossing over occurs (at that point one can see it).  Any way, the two new cells each have 23 pairs of chromosomes again, but we can't have that.  If this weird sperm cell (remember we're talking about males) was to ever fuse with an egg, one will have 46 pairs of chromosomes, and in this case, more is not better.  100% of the zygotes will abort and never see the light of day.

We humans need 23 pairs of chromosomes, that's it. No more and no less, but don't believe it isn't possible to have, let's say, 24 chromosomes.  Consider downs syndrome.

Anyway, back to our two cells.  These cells are not like the original parent cell.  These cells have different genetics to them, because of crossing over and independent assortment (refer to Mendel for explanation).  Imagine a chromsome with two separate strands attached to each other. These strands are call sister chromatids and are relatively identical to each other (at least in size).  The cell will run through those different phases I spoke of earlier and split into two new cells, but this time the sister chromatids segregated from each other into a separate germ cell.  So now we have four sex cells with 23 chromosomes in them, and not one of them is exactly the same. That's why we look so different from one another and your parents could have twelve kids and none of them will look exactly like you.  Even a twin is not really a twin.  

I know this is a little overkill, but you need this to understand the concept. Meiosis must split a cell's chromosome number in two because it is going to join with another sex cell (sperm or egg) and fuse to create a lovely zygote. The zygote will grow to create a human being.  And for a human being to be a human being, they need 23 pairs of chromosomes.  If you need to go through a detailed explanation of the phases, just visit a local textbook. My favorite is Campbell's Biology.

Just think of meiosis as a double mitosis.

The normal cells r diploid..i.e 2n. Now if they fuse to form the zygote ,it will have a 4n chromosome number which is abnormal . Therefore in order to maintain the diploid conditions in the offsprings the meiotic division is necessary so that now the cells with 'n' chromosomes i.e haploid fuse to produce diploid cells which is normal.

> Why is it necessary for chromosome number to be halved during meiosis?

That's kind of the defining characteristic of meiosis.  If this weren't happening we would call it something else and not meiosis.> What would happen to offspring if this reduction in chromosome number didn't occur?

In real life, they'd likely end up tetraploid.