The main points about phosphorus

i. Has two oxidation states readily available; (+/-) 3 and (+/-) 5.

ii. In its trivalent state (e.g. R3P:) it is very nucleophilic.

iii. Phosphorus-Oxygen bonds (particularly P=O) are exceedingly strong and often provide a driving force for a reaction.

The Wittig Reaction

Probably the most common use of phosphorus in organic chemistry is in the Wittig reaction, which uses a phosphonium ylid – formed as shown here;

The phosphonium ylid is a reasonably stabilised carbanion, as shown by the resonance forms.
The Wittig reaction involves the addition of a phosphonium ylid to a ketone or aldehyde, resulting in the formation of an alkene;

For the elimination of Ph3P=O, compare with the Peterson Olefination.
NB – the P=O bond formed here as driving force.
This reaction is highly versatile as both R and R’ can be varied, allowing creation of many new alkenes from just ketone and alkyl halide starting materials.