Angiogenesis is the formation of new blood vessels and capillaries, usually from pre-existing blood vessels. It is similar to a branching process from the blood vessel, beginning from the endothelial cells that compose the blood vessel barrier. It normally occurs during wound healing and embryonic development, but is also required for tumour growth and metastasis in cancer.
http://www.nature.com/subjects/angiogenesis
http://www.nature.com/nature/journal/v407/n6801/abs/407249a0.html