Spaying (females) and neutering (males) is the process of removing an animal's reproductive organs through a surgical procedure during which the animal is under anesthesia.  A spay for females is the surgical removal of the uterus and ovaries, and neutering for males is the surgical removal of the testicles.  The risk of mammary cancer is also reduced for female cats if they are spayed before their first heat cycle (which generally occurs around six months of age), and spraying urine to mark territories will not occur when males are neutered.  Spaying/neutering your pet is the only foolproof birth control for your cat, and it's a necessity.  There are too many strays that end up hurt in the streets or euthanised in shelters due to cat overpopulation.  When irresponsible pet owners allow their cats to roam the streets unaltered, they can end up with a female cat that is pregnant with an unwanted litter.  Then if the cats in the litter are not altered, the cycle continues.

If you adopt your cat or kitten from a shelter, most times they are either already altered or require you to follow up with them to have your new cat altered.  If they do not mention this, you should ask about services they may offer, or vouchers you can get for a low-cost spay/neuter.  A great site is Spay/USA - they will send you a voucher directing you to a clinic in your area that will do the spay/neuter for a very low cost. We got our first two cats spayed at a clinic for $150 each.  We heard about Spay/USA and contacted them before getting our third cat done - and we only paid $60 at the low-cost clinic they directed us to.

Another site that breaks down the positive points of getting your pet spayed/neutered is Why You Should Spay or Neuter Your Pet.