Here’s a nice description of the Algorithm that also explains the notion of relaxation.
The notion of “relaxation” comes from an analogy between the estimate
of the shortest path and the length of a helical tension spring, which
is not designed for compression. Initially, the cost of the shortest
path is an overestimate, likened to a stretched out spring. As shorter
paths are found, the estimated cost is lowered, and the spring is
relaxed. Eventually, the shortest path, if one exists, is found and
the spring has been relaxed to its resting length.