Enzyme Inhibition in relation to Aspirin
‘Reversible’ and ‘Irreversible’ are standard designations in enzyme kinetics. It may be that your instructor was using the word in this sense. 

As already commented, irreversible inhibitors bind the enzyme in such a way that they don't dissociate from it. Either they form a covalent bond or their affinity for the binding site is extremely high. Reversible inhibition is generally found with competitive inhibitors — those that resemble substrate enough to bind to the active site and compete with the substrate for it. Unless they have an extremely high affinity there will be an equilibrium between bound and unbound inhibitor, and the inhibitor can be competed out by substrate — i.e. the binding is reversible.

You can read about this in more detail, but still at an introductory level, in the Wikipedia article on Enzyme Inhibitors  or this section in the online version of Berg et al.