Flat Pedals can be used with normal shoes and provide you with a large grippy platform when pedalling your bike. Your feet are not attached to the pedal body via a clipless system and this provides freedom of movement on the bike.
Flat Pedals are good because they provide ease of use; no special shoe or cleat combination is required to ride a bike with flat pedals. From a performance perspective Flat Pedals are good for mountain biking disciplines such as downhill or any kind of technical riding.
Flat pedals are ideal for those not wanting to use a clipless pedal system, they provide a large grippy platform for normal shoes to grip too. You can fit toe clips and straps to some flat pedals to benefit from pulling upwards when pedalling on hills or accelerating, these tend to be more for road/commuting use. Generally the main use for most types of this pedal now is Freeride or Downhill where quick placement and removal of the foot is essential.