First Two Layers, or F2L are normally the first two bottom layers of the 3x3x3 cube, or essentially all layers up until the last layer on larger cubes.
The definition is a little different depending on the subject or who you are talking to. Normally it is as above but it may also refer to the part of the Fridrich method that solves the pairs without counting the cross part.
Approaches
Petrus F2L
Another way to solve the 'F2L' is by building blocks, common during the first two layers of the Petrus method.
Fridrich F2L
There are many ways to solve the 'F2L' on a cube. A common system is using the Fridrich method first two layer approach. After solving the cross, a corneredge pair is paired up, and then inserted into the correct slot. A total of four corner edge (or 'CE') pairs are made and inserted to solve the first two layers.
The concept of pairing up four corner/edge pairs was first proposed by Ren Schoof in 1981.
Most people agree that the Fridrich F2L should be done intuitively, but when you are starting out it can be instructive to see some optimal solutions for each F2L pair. Below is a collection of such optimal solutions
Easy Cases
Reposition Edge
Reposition Edge and Flip Corner
F2L 9

F2L 10

F2L 11

F2L 12

F2L 13

F2L 14

Split Pair by Going Over
F2L 15

F2L 16

F2L 17

F2L 18

Pair Made on Side
F2L 19

F2L 20

F2L 21

F2L 22

Weird
F2L 23

F2L 24

Corner in Place, Edge in U Face
F2L 25
Back Right slot open  (U D' R U' R' D)

F2L 26

F2L 27

F2L 28

F2L 29

F2L 30

Edge in Place, Corner in U face
F2L 31

F2L 32

F2L 33

F2L 34

F2L 35

F2L 36

Edge and Corner in Place
F2L 37
Solved

F2L 38

F2L 39

F2L 40

F2L 41

F2L 42

See Also
External Resources