Cladistics is the method of classifying organisms into groups called clades. Clades consist of an ancestor organism and all of it's decedents and one branch is the tree of life. Cladograms are diagrams that show relationships within a clade.
So cladistics is a mechanism or a method that scientists use when they're trying to figure out who is most closely related to whom. And it's a way of grouping organisms based on looking at what are called derived characteristics which are groups or types of characteristics that are unique to a particular group of organisms. So you'll wind up with thing called clades. A clade is a group of related organisms that all have a shared derived trait or shared derived traits. Examples of a clade would be like for example mammals. All have mammals have hair and mammary glands. So I as a mammal have hair, nonfunctional mammary glands, but I do have them. Even whales have hair; eight of them and mammary glands. Now, you'll see the term derived traits like I mentioned before and these are unique or new traits that all members in a clade all share with each other and their immediate ancestor. You'll know often see these diagrams that are sometimes called cladograms and here is an example of a cladogram that shows some common ancestor to all these organisms and that common ancestor may have been some kind of four-limbed fish or something like that. From that, we can see the frogs but derived off a derived trait that all these organisms share that aren't shared with the frog is the amniotic egg. Whether it's the shelled eggs of the lizards and the crocodiles or the amniotic sac that humans use to give birth to help keep their child alive inside of the uterus. From here you can see that mammals and humans branched off with their and mammary glands, while the scaly skins of these reptiles is a derived trait that all of them share. However we can group the crocodiles in their own little sub-group or subclade because they have a gizzard which lizards don't. That's cladistics.