Binary trees are data structures where every node has at most two children, a left and right child. A binary tree has a root node at the top and leaf nodes at the bottom with no children. The depth of a node is the length of the path from the root to that node, while the height is the length of the longest path between the root and a leaf plus one. Binary trees can be full, complete, or fully complete depending on how nodes are distributed. Common operations on binary trees include searching, summing nodes, and traversing them in inorder, preorder, or postorder sequences.