the word height in this term refers to the height of the tongue when the vowel is pronounced. There are two different systems to classify vowels this way, which use the terms close, open, and mid-close/mid-open, or high, low, and mid. The terms close and high refer to the fact that when a certain vowel with these qualities is pronounced the highest point of the tongue is as close as possible to the roof of the mouth. The terms mid-close/mid-high and mid refer to the fact when certain vowels are pronounced the highest point of the tongue is somewhere between the roof of the mouth and the bottom of the mouth. The terms open and low refer to the fact that when some vowels are produced the tongue is as close as possible to the bottom of the mouth.
Matthews, P. H. The Concise Oxford Dictionary of Linguistics. Oxford: Oxford University Press, 1997.