A "thread" of conversation would be a single chain of A, B, C, D where D replied to C which was replying to B replying to A. All linear, with exactly one response to everything except the last post.

A tree, on the other hand, branches. For example, The original post gets 3 replies (A, B, C). Three more replies are made to A (A1, A2, A3), nobody replies to B, and C gets one reply (C1).

You can see this in the layout of the posts, with each level of the tree indented slightly further, and the "Re^N" subject lines incrementing with depth by default. Re^3 is replying to the closest Re^2 above it.