Yagi Antenna: A directional antenna, meant to propagate signal in a specific direction rather than to spread it all around. These are commonly used in bridging applications, where two wireless bridges are separated by a great distance and direct their signals at each other to establish a point-to-point link. Yagi antennas are generally stronger than patch antennas, which are a different kind of directional antenna.
Omni Antenna: An antenna that covers 360° around itself, providing service to all clients in an area. These are almost always used when supplying coverage to clients, but they can also be used in point-to-multipoint bridging applications. The coverage is not a sphere, but looks more like a donut, with coverage 'gaps' directly above and below the antenna (assuming it's oriented vertically).
Dipole Antenna: This is essentially an omnidirectional antenna, but it's commonly referred to in wireless as a refrence point to relate other antennas. The reference point is supposedly a theoretically perfect antenna, with signal being generated from a single point in space with a perfectly spherical coverage. Since it's theoretical, this kind of antenna doesn't exist, but all real antennas can be compared against this and given a value.