Transitional fossils are fossilized remains that exhibit traits from two groups - an ancestral group and a descendant group. Because of this characteristic, they can be used to construct phylogenetic trees, and determine how one species is related to an older species. This can particularly be a lot of help when a common trait is found in a descendant/derived species and an ancestral group where the descendant species has a very different mode of living or gross anatomy from the older group.
The relationship between the ancenstral group and the descendant group, however, is not clearly claimed to be a direct due to the fact that evolution is a branching process, and that the point of divergence cannot clearly be identified, particularly how near or how far the transitional species is from the point of divergence.
Nonetheless, these transitional fossils serve as evidence to Darwin's Theory of Natural Selection as conserved traits are proven to survive the test of time. This also supports evolution in a way that is shows gradual change in traits of species over generations due to change in living conditions.
An example of a transitional fossil is the Austrolaphitecus afarensis. This fossil is a hominid which has the traits of both the quadrepedal ape ancestors and modern bipedals.