An elimination reaction involves the removal of two species from a molecule:

The most common type of elimination is a so-called 1, 2- elimination where the two species are removed from adjacent carbon atoms, usually causing the formation of a multiple bond. For example;

This 1, 2- style elimination can happen in one of three distinct mechanisms, labeled using a similar system as nucleophilic substitutions.

E1

This stands for Elimination with a unimolecular RDS.
An example;

So, the C-X (in this case C-I) bond is broken first in the RDS, then the base present (OH in this example) takes the H+ to complete the elimination of HX. Note that the RDS is exactly the same as for SN1, so cation stability aids E1 mechanisms. (Also, as with SN1, the unimolecular RDS will cause first order kinetics.)

E1CB

This is very similar to E1, except this time the C-H bond is broken first rather than the C-X bond (this implies that the RDS is again the loss of X, not the initial loss of H). The CB stands for conjugate base, the species from which the elimination occurs.
An example;

Unlike E1 (and SN1), what is important this time is the stability of the carbanion, or conjugate base. In this example, the carbanion is stabilised as an enolate, but if there were no stabilisation available, it would be much more likely to follow the E2 mechanism. In fact this reaction mechanism is the least favourable of the three, and for reactions such as the example above, the energy of activation for E2 is lower than that for E1CB.

E2

This surprisingly stands for Elimination with a bimolecular RDS.

This is the most commonly observed of the three elimination mechanisms. As with SN2, there is a single TS including all the species involved.