Platinum is the game's premium currency, it is used for buying items in the store, accelerating builds and upgardes and aids your progression in the game. Some items are only available via Plat. (as it's called by players of the game).
Platinum can be gifted, won, earned (through surveys etc) or bought (with real cash).
To be gifted by one player to another the gifting player must select this option when buying new platinum, they can not gift from their existing platinum. They must also be in the same alliance as you.
It can be won through player tournaments on the map, Kabam events, or Zoots Jackpot.
You can take surveys or watch adverts to earn some (generally very little).
You can buy platinum with actual real cash.
Controversially it has been hotly debated on the kabam.com forums that depending on where you live, the amount Kabam charges for this platinum differs, if you are in the UK you may pay more than others (the USA for example) pay for it.