Q:

If my world is flat (obviously not possible) how would I explain the edges?

I don't want my world to be infinite, that would be a pain to draw maps for. And I need it to be flat (for a slightly unrelated reason). How would I explain why no one has looked over or seen the edge before? I could always put a giant wall there, but that just makes more questions than answers ( i.e. who built it)? 

A:

I can think of at least two reasons. 

The physics answer, If your disk is massive enough you get an interesting effect that causes it to behave more like a bowl than a disk even though it is flat, at least as far as gravity is concerned, the closer you get to the edge the steeper the surface feels. to a person on the surface it would feel like climbing a very steep mountain. 
Try this vsauce video (0:30 to 2:00) for a more visual feel for what I am talking about. 
the discworld answer, the edge is entirely one giant ocean waterfall going over the side, anyone who sails too close to the edge gets dragged over the side to their doom. So it is not that no one has ever tried it is just they have never survived the attempt. 

A:

Make your world finite but spatially bounded. This means anyone walking towards where the edge would be will find themselves inexplicably turned around, even though they were still walking in the same direction and to their own minds they didn't turn around. They will arrive back at the place where they started.
The Arthur C Clarke short story "Wall of Darkness" uses this concept. It also has a wall, the existence of which is never explained, but possibly it was built during an earlier time to stop people having the inexplicable experience of finding their world was spatially bounded. I suspect Clarke was putting a science-fictional twist on the sort of flat-earth world that appeared in various fantasy short stories by Lord Dunsany. Clarke was a fan of Dunsany's fiction.
The concept of finite but bounded space appears in certain versions of cosmology. It is quite reasonable to use it for what is essentially a fantasy world. There is no need to explain how and what it is, just show what happens when people reach the "edges" of their world. Effectively they never get there.
This also explains why no-one has looked over the edge. They can't get there to do it.

A:

Gravity to the rescue.
If your planet has a disc-shape, gravity will be different towards the edges as compared to the center. The habitable zone on the planet would be near the center (maybe on both sides, that might make for interesting story material...) while the more you go towards the edges, the more everything becomes inhospitable, to the point that the atmosphere is too thin to reach the edge without some kind of space suit, which depending on the time period of your story may be far in the future.

