When a doctor cannulates a patient, she inserts a very thin tube into the patient's body. A common reason a doctor might cannulate someone is to give them I.V. fluids.
If you've ever had medication administered intravenously — in other words, directly into a vein — your doctor or nurse had to cannulate you first. The extremely tiny tube used in medicine for I.V. drugs or drawing out blood or other fluid is called a cannula, a word that means "small reed or pipe" in Latin.