Someone who is tidy likes everything to be neat and arranged in an organized way.

Something that is tidy is neat and is arranged in an organized way.

When you tidy something away, you put it in something else so that it is not in the way.

When you tidy up or tidy a place up, you put things back in their proper places so that everything is neat.

When you tidy a place such as a room or cupboard, you make it neat by putting things in their proper places.