There are two sources for presents. First, every time one of your alliance members buys a pack, the full alliance will get a present based on the pack the member bought! Second, each time you or any of your alliance members makes a final blow on a mob on the world map, you will get a present with crafting materials, resources, speedups or even diamonds. This can help free to play players to grow
The max number of gifts than can be held is 300 so make sure to visit the alliance tab and claim on a regular basis, in an active this could mean several visits a day.
Not only do you get materials, diamonds and speed-ups but each chest opened gives keys to the alliance, once enough keys have been collected the next level will be unlocked, so it's VERY important you check this tab and claim all chests.