A tree is a graph that has n nodes and n-1 edges and is connected with no cycles.
Additional Terms
A forest is a graph that contain no cycles (collection of trees) and a rooted tree is a tree where one vertex is designated as the root.
Edges in a rooted tree can be assigned a direction, pointing away from the root which is called a directed tree.
Binary Trees
In a complete binary tree, each vertex has at most 2 children. Each level also needs to be filled before the next level to keep things balanced.