What's the purpose of a heated bed in a 3D printer? Is it worth the extra money?

Second question first: I would not buy a 3d printer without a heated bed.

A very common issue with FDM printing is bowing or curling. The printer lays down a first layer of hot plastic, then another, then another, and so on, building up the shape being printed. But there’s a problem. As you may recall, when things cool down, they shrink. For upper layers on a piece being printed, they’ve got adhesion with the lower layers to keep them in place, but the bottom layers don’t have much to keep them from shrinking, so they do, curling up from the edges. When I first started 3d printing, everything I printed had a curved base. Everything that was supposed to be flat would rock back and forth. There are all kinds of suggested solutions for better adhesion to the print bed, fiddling with fan settings, and so on to reduce curling, but it never helps as much as you’d like.

Then I retrofitted a heated bed to my printer, and the problem went away. Completely and instantly. I went from pieces two or three inches long which had a height difference of two or three mm between edge and center to being able to print completely flat from one end of a 10 inch print bed to the other. See, the heated bed keeps those early layers warm enough long enough that they don’t shrink and curl up. It solves the curling problem in ways that painter’s tape and glue stick on print bed won’t. That saves a lot of time, a lot of frustration, and a lot of money on the back end by not having to toss out failed prints which curled too much and having to use more filament until it works out. Bowing/curling is a big problem without a heated bed, and not a problem with it. It isn’t just worth the extra money; a 3d printer without a heated bed isn’t worth any money.