How can I summon a meteorite?

I've heard people talk (or at least, saw them write on forums) that they summoned meteors to create meteorite weapons and armor.

How do I exactly spawn these meteors and what can I make out of meteor?

Meteors can fall naturally (but fairly rarely) in game, but can also be summoned by breaking shadow orbs. These orbs, which are purple looking and float around can be found at the bottom of chasms in areas of corruption, and can be broken with hammer type weapons, or dynamite. For more info, see this wiki page: Shadow Orb

As for what can be made, this is from the wiki: http://terraria.gamepedia.com/Meteorite_Bar

Meteorite bars are made from six meteorite ores. Meteor bars can be used to create the much coveted Hamaxes, Space Guns, Star Cannons and Phaseblades. They are also used for making meteor shot which is ammo like musket balls but stronger, and Meteorite Armor.