Seasoned wood means that the moisture content in the timber has been reduced to an appropriate level for the intended use of the wood.
The moisture content will naturally drop in any wood but usually so quickly that checking or warping occurs as a result of shrinkage in the grain. With seasoned wood it has been reduced at a controlled even rate through the whole of the wood, which basically allows the core to shrink at the same rate as the outside, thus avoiding stresses which lead to cracks.
If done properly, in most cases, the moisture content in the wood will drop without causing any cracks or warping and also resulting in a more stable piece of timber.