Most likely your cat has hyperthyroidism, which is most common in cats over the age of 10. The thyroid is a gland located near your cat's windpipe; with hyperthyroidism, the thyroid becomes over-active and produces too much of the thyroid hormone (this hormone regulates metabolism and organ function). Untreated, hyperthyroidism can lead to heart or kidney failure, and can be fatal. However, there are three methods of treatment (antithyroid drugs, surgical removal of the thyroid, and radioactive iodine treatment that disables the gland); typically, vets go with the antithyroid drugs, which are relatively inexpensive (although your cat will be on them for the rest of his or her life) and work pretty well -- I believe the other 2 treatments are for more serious cases, or are if the drugs don't work.
My parents' cat has hyperthyroidism (which is why I know so much about it!), and they first noticed it when she started gaining a LOT of weight all at once. She's a very small cat, so it was noticeable. She's on the antithyroid medication and it's worked wonders for her; in fact, every cat I've known that had this problem responded well to medication. It's serious because, if left undiagnosed and untreated, it can be fatal, but my parents' vet told them that, of the diseases cats get as they age, it's one of the easier ones to treat. I wouldn't worry about it too much, so long as you follow your vet's instructions and monitor your cat's condition.