Directional antenna (e.g. satellite dish) broadcasts power in some specific directions (space angles) around the antenna (which are called main-lobes). This is to increase the chance of picking up the signals at the receiver (which is also pointed at the transmitter antenna).

Omnidirectional antenna on the other hand, transmits information in all directions (kind of like a sphere around the antenna). The transmitted power per surface is identical at a certain distance, and for the same input power, power density of an omnidirectional antenna is less than that of a directional one.

Complete omnidirectional antenna doesn't exist in practice, but sources like the Sun and wireless modems (some of them) come close to this definition. BTS towers on the other hand, make use of directivity methods to further cover the area, which is why you see something called SAR (Specific Absorption Rate) on your smartphone's box. In layman's term, SAR measures how much EM power your body-flesh absorbs because of your phone, and as you might guess, the less SAR, the better.