Most modern hearing aids fitted today automatically switch between omni setting and directional setting, via a pair of omni mics and a time delay.
Put simply; the directional mics allow for certain areas to be made quieter in certain directions: this is controlled either via the software or via the remote/buttons.
Predominantly, most systems will not quieten the area ahead of you as it's deemed that you want to hear most from the front. Some systems are able to move the quieter areas around to track noise sources and keep them lowered. In addition to this the best systems can isolate and reduce the noise sources in a given direction AND frequency band so that they detriment the overall speech signal as little as possible. When this is done properly using the combined feed of sound from both ears through binaural directionality, it can be hugely effective in improving the signal over background noise.
So, why would you ever want to be in Omni set-up?
Omni mics tend to have a flatter frequency response in that they are more effective at lower frequency where the directional mics tend to become self damping. When listening via directional mics, the effective range of the system (in improving the situation) is 6-12 feet. Beyond this distance the directional advantage is lost and room reverberation can become counterproductive. Omni mics aren't subject to this, so the brain can sort out the reverberation issues by itself.
So, if you're in work, at a dinner, a store or another noisy situation where you need to hear what's going on - directional systems are the best. However, if you're at home, taking a walk in the country or listening to music, you might well find that the Omni set-up is preferential.
Any half-decent system will automatically switch between at least two modes of Omni/Directional performance.