“Flagellate” is a catch-all term for protists with 1 to a few (typically 4 or less) flagella. The eukaryotic flagellum is a completely different structure from the bacterial flagellum. Bacterial flagella are made from a protein called flagellin, and are turned by a rotary motor embedded in the cell membrane. Eukaryotic flagella are instead composed of microtubules (assembled from the protein tubulin), and they move by bending. This bending is powered by motor proteins called dynein that are attached to the microtubules in the flagellum itself. For this reason, some scientists prefer to call it the undulipodium, to emphasize the difference from the bacterial version.
Flagella are used for different functions. The variety of kinds of flagellar motion is illustrated by Rosemary Arbur on the Protistiary website (mouse-over for animations). Aside from swimming, they can also be used in feeding and in sensing the external environment.