Why is agreement between the fossil record and phylogenies constructed from living organisms considered strong evidence of evolution?

Both of those two independent methods of investigation resulted in the same pattern which means it is significant.

Fossil records explain the history and evolution of life based on fossils. Fossils are remains of organisms preserved in sedimentary rock. In fossil records they are analyzed and arranged chronologically and in taxonomic order, so that can represent the evolution.

Phylogenies describes the relationships between organisms (species) : from which organisms it is evolved, to which species it is most closely related etc.

It is used to organize living organisms into specific categories.