Trees are fundamental data structures that combine advantages of ordered arrays and linked lists. They consist of nodes connected by edges, where nodes often represent entities and edges represent relationships between nodes. Common tree operations include traversing to visit all nodes in order, searching for a node by its key, and inserting or deleting nodes. These operations have O(log N) time complexity where N is the number of nodes. Binary trees restrict each node to at most two children while Huffman trees are used to compress data by assigning variable-length binary codes to characters based on their frequency.