Definition from CancerWEB's On-Line Medical Dictionary:

The process of vascularisation of a tissue involving the development of new capillary blood vessels.

My layman's definition:

Essentially, this process involves the growth of new blood vessels to supply blood to parts of the system that require it. This occurs mostly during gestation of a foetus, wherein the foetus is developing the capillaries it will require to supply blood to all vital systems. This occurs in the formation of cartilage during the youngest years of formation, but is then stopped by the release of angiogenesis inhibitors (see Thalidomide, Endostatin) in the system which cause the cartilage to harden and kill the capillaries running through it.

NOTE: There is a request in for a name change on this node, so it should go through shortly.