SSD's are the current type of hard drives in computers. Apple Computers use these types of drives now, with some having the option to choose a regular / older type mechanical hard drive instead. Or a combination of both, known as a Fusion drive.
The number is the size. 128 refers to 128GB. Depending on what model of Mac we are talking about you can choose to upgrade to different sizes during purchase.
If this is a used Mac, then the upgrade possibilities will depend on the exact model year of the Mac.
Beyond that, while it's technically possible to upgrade SSDs in Macs post sale, in newer ones it's a little more cumbersome, and generally will void the warranty. Since you'll need to disassemble it completely to get to the hard drive. Also the newer SSDs Apple is using, are hard to come by in the seocndary market in larger sizes, and can be very expensive.