A phylogeny (phy·log·e·ny, plural: phylogenies) is simply a way to represent the evolutionary history and relationships among a group of organisms. This is often represented in a branching diagram, or a 'tree'. See repersentations of this below.
Maximum Parsimony: method used in phylogenetic analysis that prefers the simplest tree, or the one with the fewest evolutionary changes, as the most likely explanation for the observed data. (least number of nodes)
Sister Taxa: are two groups (species, genes, etc.) that share an immediate common ancestor and are each other's closest relatives on a phylogenetic tree. ‘Pairs’ on a phylogenetic tree.
Synapomorphies: are shared, derived traits or characteristics that are present in two or more taxa and their most recent common ancestor, but absent in more distant ancestors.
A monophyletic group (clade): consists of an ancestor and all of its descendants, representing a complete branch on the tree of life.
Paraphyletic group: includes an ancestor and some, but not all, of its descendants, leaving out one or more groups that share the same common ancestor.