A form of writing whereby some letters in a word are replaced by a numerical likeness or other letters that create an identical or similar sound.
This style of writing was originally in use by hackers who were attempting to bypass word-filtering on mail servers. For instance, they would use the term 'haxorz' to replace 'hackers'. Internet users new to hacking adopted the style in an attempt to emulate those more experienced, and usage became widely spread.
In recent times the method is almost never used to avoid word-filtering software, but rather to satirise script kiddies
and 12 year olds, or to abbreviate for faster typing. It's interesting to note that in most cases it takes more time to type in leetspeak (due to the constant swapping between numbers and letters) than it would take to just type the words properly.
When using leetspeak, you should be aware that you are almost definitely coming across as a moron