The word means one bound, a bondsman (Latin, ligo, to bind); hence, vassals were called liege-men - i.e. men bound to serve their lord. The lord was called the liege-lord, being bound to protect the vassals.
“Unarmed and bareheaded, on his knees, and with his hands placed between those of his lord, he [the military tenant] repeated these words:`Hear, my lord, I have become your liegeman of life and limb, and earthly worship; and faith and truth I will bear to you to live and die.” —Lingard: History of England, vol. ii. chap. i. p. 27.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Liege from Infoplease: