This is a bifurcating tree. The vertical lines, called branches, represent alineage, and nodes are where they diverge, representing a speciation event from a common ancestor. The trunk at the base of the tree, is actually called the root. The root node represents the most recent common ancestor of all of the taxa represented on the tree. Time is also represented, proceeding from the oldest at the bottom to the most recent at the top. What this particular tree tells us is that taxon A and taxon B are more closely related to each other than either taxon is to taxon C. The reason is that taxon A and taxon B share a more recent common ancestor than they do with taxon C. A group of taxa that includes a common ancestor and all of its descendants is called a clade. A clade is also said to be monophyletic. A group that excludes one or more descendants is paraphyletic; a group that excludes the common ancestor is said to be polyphyletic.

This figure shows several monophyletic (top row) vs a polyphyletic (bottom left) or paraphyletic (bottom right) trees. from http://evolution.berkeley.edu/evolibrary/article/side_0_0/evo_06
The video below focuses on terminology and explores some misconceptions about reading trees:
Misconceptions and how to correctly read a phylogenetic tree
Trees can be confusing to read. A common mistake is to read the tips of the trees and think their order has meaning. In the tree at the top of the page, the closest relative to taxon C is not taxon B. Both A and B are equally distant from, or related to, taxon C. In fact, switching the labels of taxa A and B would result in a topologically equivalent tree. It is the order of branching along the time axis that matters. The illustration below shows that one can rotate branches and not affect the structure of the tree, much like a hanging mobile:

http://evolution.berkeley.edu/evolibrary/article/%3C?%20echo%20$baseURL;%20?%3E_0_0/evotrees_primer_08

