Search is perhaps the key organising principle of good old fashioned AI GOFAI. One of the key trends in GOFAI is that it's symbolic. That is the knowledge is represented by symbols, and you can derive new knowledge based on rules. This fits in with Newell's Physical Symbol System Hypothesis; every intelligent being has a symbol system.
Search relates particularly in discrete systems. You can search in continously varying spaces, but a lot of the search algorithms are designed for discrete spaces.
Imagine moving around a chess board with walls. That's discrete space search. You can use this search space as a metaphor. You can define other (non-geometric) domains as spaces. Solving the problem can be done via searching through that space. Search spaces, thus, provide a really good and widely general way of thinking about and discussing problems.