Best first search:

Best-first search is a search algorithm that explores a graph by expanding the most promising node chosen according to a specified rule.

In BFS and DFS, when we are at a node, we can consider any of the adjacent as the next node. So both BFS and DFS blindly explore paths without considering any cost function. The idea of Best First Search is to use an evaluation function to decide which adjacent is most promising and then explore.

Best First Search falls under the category of Heuristic Search or Informed Search.