"Omnidirectional" is generic term for an antenna that radiates equally well in all directions. There are several antennas that are considered omnidirectional.
1/2 Wavelength Vertical
Most folks lump all vertical omnidirectional antennas into the same category and call them "Ground Planes". A ground plane antenna is actually an antenna similar to the vertical dipole. Shown in figure 1, you can see the hollow tubing is now instead brought out at a 45 degree angle (and split into 3 sections) out from where it is on the vertical dipole. These rods are usually called "radials". This type of antenna is really not a very high gain antenna.
A ground plane antenna.
A much better type of antenna that has more gain is the 1/2 wavelength vertical (Shown in figure 2). We know that the impedance of the 1/2 dipole is 70 Ohms when we attach the coax in the middle, but what if we were to attach our coax directly to the end? The impedance at this point is high, very high, so we must make a matching device to match the antennas impedance to the 50 Ohm coax. What would happen if we did not use this matching device? Well if you have been reading along, you would know that this would result in a very very high SWR.
There are several commercial 1/2 vertical antennas available, the two that I can think of most easily is the Solarcon A99 and the Shakespeare Big Stick. They provide slightly higher gain than the vertical dipole antenna.
The bandwidth of these antennas are good, they can easily span all the CB channels and more with a low SWR.
5/8 Wavelength Vertical
A higher gain antenna than the 1/2 vertical antenna is the 5/8 vertical antenna. As we can figure from the 5/8 wavelength rating the antenna is about 22 feet long (5/8 of 36 feet). This antenna is similar to the 1/2, it needs a matching device at the base to match it to the coax, it cannot be attached directly. This antenna has about 1.2 db gain over the dipole antenna and 1/2 vertical. Figure 2 shows both a 1/2 Wave vertical and a 5/8 Wave vertical antenna. It achieves this extra gain by concentrating its pattern out more at right angles from the antenna instead of wasting signal at high angles, see figure 3.
I have just heard Solarcon is coming out with a new 5/8 antenna (its about time, this antenna design has been around since the beginning of time!). There are several 5/8 antennas, Hustler 27JR, Antenna Specialist Sigma 5/8, Maco V 5/8. They offer slightly higher gain (about 1.2db) than the popular A99 and Big Stick. Shakespeare was committing a crime claiming their ABS 1600 5/8 wave antennas had 12.5 dbi gain (the "i" means over an isotropic antenna). This was plain ridiculous. A 5/8 wave antennas is a 5/8 wave antenna. Do you think a vertical could have more gain than a beam? Never! This is the perfect example of how out of hand antenna manufactures have gotten with their advertising. Now, everyone thinks their A99 is a low gain piece of junk because Shakespeare claimed 12.5 dbi with their "new" antenna. Shakespeare no longer claims the ABS 1600 has 12.5 dbi gain, but everyone who sells it is still advertising that gain figure.
Even if you do not know the manufacture or anything about the antenna you are looking at, you can tell if the antenna is a 1/2 or 5/8 wave by its length, again 1/2 is about 18 feet and 5/8 wave is about 22 feet (at CB frequencies).