Why is seasoning of timber important?

It's to dry out the wood before you use it. When wood dries it shrinks. If you use it fresh and make, say, a cabin, over time the wood will dry, shrink and you'll get warping, splitting, or - worst - gaps. If you pre-shrink the wood (seasoning), then the wood will remain the same after the cabin is built.

Also, seasoned wood is stronger, lighter, doesn't attract insects so much, and is easier to work with.