A simple example of a phylogeny is a family tree where the leaves of the tree represent the children in the family and branches represent relationships between parents and children. The tree represents different clans inside a larger family.
Likewise, a language phylogeny is a tree representation of the closeness of various languages. Dutch and Flemish are sister-languages that have a very close common ancestor. English is a cousin language, which is a bit further away from Dutch and Flemish. The Scandinavian languages are far cousins.
The place where lines come together in the language ‘family tree’ represent older languages that gave rise to the child languages in the tree.
Below, an example of a phylogeny for ancient languages (From Ringe).