A lot of trees seem to have a long thick trunk that grows up to a certain point and then splays out to any number of branches above. Is there a term that refers to this section.
Well, one term is the Crotch.
Fork
My orchardist grandfathers used crotch (and, hence, so do I). Branches could “fork” beyond that, but the primary, major area of branching was the crotch.
I call it the crotch.
It’s a crotch. I think.
I think we’re approaching consensus.
Yep, thread’s over. Stick a fork in that crotch.
OUCH!
Crotchfork…band name!
It’s probably worth noting that all (or almost all) the trees in question are dicotyledenous angiosperms. A wide number of dicot families have evolved tree forms; nearly every “tree” is either a dicot or a conifer, the order that constitutes almost all of the living gymnosperms. (Only palms, which are monocots, and the ginkgo, the only extant nmember of another gymnosperm order, are exceptions to this rule AFAIK.)
The technical term for a tree’s general shape is its habit – and most people recognize tree habits without conscious thought. E.g., handed sillhouettes of an elm, a willow, and a spruce, most people could identify which is which by the general shape without seeing leaves, bark, etc. Typically, trees are comprised of a root system, a trunk, and a crown. The trunk’s function is to hold the crown up where it can compete for sunlight and to connect it to the roots, the latter being an important element in a tree’s physiology, as it transpires. (Pun intended.)
Nearly all the conifers and several families in the dicots, including the birches and poplar/aspen group, have habits in which the trunk extends virtually to the top of the treee, with large branches mostly coming off it. While the branches themselves may bifurcate, trifurcate, etc., the trunk does not.
In contrast to this, many trees, the apples and many maples being good examples, tend to have the trunk bifurcate or produce multiple major branches at the base of the crown. By analogy to a person standing on its head, the point where the trunk bifurcates into limbs is the crotch. Forks are wherever limbs bifurcate; the crotch is a fork, but not all forks are crotches.
You win! Go with the consensus concept. At least Dumbguy won’t just freak out when the term “fork” is unwisely used for the concept.
Crotch Nazis! 
It’s incorrect, however. A “crotch” is any point where a branch joins a trunk, or two major branches join.
The point above the ground at which many branches splay out is (unsurprisingly) called the branching point.
Crotch was the word I was thinking of. For some reason I had ‘notch’ stuck in my head.
Nice post, Polycarp. In my head I see you smoking a pipe as you type.