All cells need a constant source of oxygen and nutrients to survive. These nutrients are delivered to cells via the blood through blood vessels (such as veins, arteries and capillaries). Since cancer cells are rapidly dividing and growing, they need an extra supply of blood to be able to grow. This means tumors need access to extra blood vessels that can feed them with these nutrients. The way in which tumors acquire these extra blood vessels is called angiogenesis.
Tumors develop the ability to release special signals that stimulate blood vessels growth. These signals are called angiogenic factors. Once nearby blood vessels are stimulated by angiogenic factors, they begin to grow extra vessels that penetrate the tumor. The extra supply of blood "feeds" the tumor with nutrients to aid its rapid growth.
In this manner, the tumor "tricks" the body into creating new blood vessels. The blood vessels created in this way are not exactly the same as normal blood vessels: they are usually less organized and leakier than normal vessels.