Meteorite Ore comes from Meteorites, which have a chance of appearing each night at midnight after a Shadow Orb (Or Pulsing Heart) has been broken. The amount of Meteorite Ore that appears depends on where the Meteorite lands, as Meteorite Ore will replace existing blocks rather than creating new blocks. For this reason, it is recommended that you not build any Skybridges until after you no longer need Meteorite; if a Meteorite hits a Skybridge, it will not have many blocks to replace therefore little Meteorite Ore will be made.
Meteor Heads have a 2% (1:50) drop rate of Meteorite Ore. If you continuously want to farm the ores then this is a slow, but possible process.
Tips and Tricks
Keeping the Meteor Heads in front will allow the player to continuously knock them back while mining.
Only a certain number of Meteor Heads (usually 3 to 6) will spawn at a time, unless the player is unfortunate enough to attempt to mine during a Blood Moon, in which case they will spawn in overwhelming quantities.
Once there is less than 50 Meteorite Ore placed in the immediate area, the "Eerie" theme which normally plays around Meteorite deposits will revert to normal and Meteor Heads will cease to spawn.
When a player is in a Meteorite biome, only Meteor Heads will spawn, unless you are also in an Ocean biome.
The player can place 50 Meteorite Ore to create an artificial Meteorite biome, which has the same properties as a natural Meteorite. This can be done to prevent more dangerous monsters from spawning.
It is possible to gather all of the Meteorite Ore without an Obsidian Skull as long as the player does not directly touch the Meteorite blocks.
Using Dynamite to destroy most of the Meteorite Ore at once will make it easier to collect it, as well as stopping the Meteor Heads from spawning much sooner.
Using Bombs is also an alternative to using Dynamite as it is much cheaper, and also due to the fact that they can be made into Sticky Bombs. Using Sticky Bombs allows you to position where you want the explosion, as you do not have to worry about bouncing. The only downside to this method is that it takes longer to mine the Meteorite as Bombs lack the large explosion radius of Dynamite.
Standing on the Meteorite with strong armor helps to be able to ignore the heads that appear, though by the time you can safely use this technique, you won't have much use for Meteorite.
Meteorite Ore will still burn you even if submerged underwater.