An oversized closet is a larger than normal closet. While a normal closet can be anywhere from three feet to eight feet long and two to three feet deep, an oversized closet can be much bigger and create more storage space.
It seems that bigger is often better and in this case, it's mostly true. Having an oversized closet means you'll have more room to store belongings, so you'll likely have room for more than just clothes. It's also great if you're sharing your closet with a roommate or significant other.
But the square footage for a larger closet needs to come from somewhere, usually your bedroom, living room or other parts of your apartment will be a foot or two smaller to give more room to your closet. Closets can also become messy quite easily and with a bigger closet comes a bigger mess. Most apartments with oversized closets will charge a higher price, too.
Oversized closets are great for extra storage space, but you need to weigh the pros and cons to decide what you're willing to give up to have one. And of course, not every apartment will offer one anyway.