N-gons are polygons with more than 4 vertices.
They can be VERY useful when doing architectural stuff for example or also when dealing with complex geometry before doing some clean-up.

As Loloallo said they can mess up the mesh when animating so they aren't recommended when animating.
Cheers,
Laurent aka Tartiflette
Edit : Oops, Piem's reply has completed Loloallo's answer quite well already !