Omnidirectional microphones pick up sound from all directions equally, whereas Directional microphones focus more on one direction than others.
For microphones that are used very close to the source -- such as earsets, headsets, and head-worn lavaliers -- the omnidirectional pattern is usually the best option since the proximity to the source provides ample gain-before-feedback.
For microphones used farther from the source -- such as hanging choir or podium mics -- or in situations requiring extreme isolation -- floor monitors or speakers nearby (5ft of less), very loud environments -- choose a directional microphone with a cardioid or hypercardioid pattern.
Something to consider: Directional microphones are very sensitive to wind noise and handling noise. Windscreens and cable clips/tape are highly recommended to help reduce wind and handling noise.
Omnidirectional microphones pick up sound from all directions equally.
Cardioid rejects more ambient noise compared to an omni while providing a wide front-lobe for flexibility in placement.
Hypercardioid provides the most rejection of ambient noise but has a narrower front-lobe.
Bidirectional picks up sound equally from two directions, and are commonly used in mid-side recording setups.