2048 is the maximum number of pixels that your image can be, either in height or width. More about pixels here. I use the professional standard of 72 pixels per inch, so a photo that is 720 pixels wide displays on a web page at ten inches wide. Hey, I never said that I was good at math! If you are good at math, you can see that 2048 pixels is pretty darn big. So the image will be razor sharp even on the biggest monitors. On normal size monitors, like my iMac, it is more than generous.
When you optimize a photo, which is best done in Photoshop, use Save for Web. Select Maximum for quality, and 2048 for image size. Don't worry about the other number, as long as you have constrain proportions, it will be OK.
By the way, this is the new standard for Facebook, too.