Sampling-based planners: build a network of reachable points
Sampling-based planners tackle the search problem by not searching everywhere at once. Instead they randomly sample many candidate points in the configuration space, the space of possible robot positions or joint angles, and check whether each new sample can be connected to the growing structure without passing through an obstacle. Valid connections are added as edges, gradually building up a tree or graph of reachable configurations until some branch reaches close enough to the goal to complete a path, as sketched in this lesson's code snippet for a tree-growing approach.
The appeal of this approach is that it scales reasonably well to complex, high-dimensional spaces where exhaustive search would be hopeless, because it never has to reason about the whole space at once, only about whether each new random sample is locally reachable. The tradeoff is that the found path isn't guaranteed to be optimal, it's just a valid path that the random sampling happened to discover, and it's often jagged or roundabout unless a smoothing step is applied afterward.