Avalency refers to the property of a verb of taking no arguments. Avalent verbs are verbs which have no valency, i.e. they have no logical arguments, such as subject, object, etc. A common example of such verbs in many languages is the set of verbs describing weather.
It rains.
It snows.
It is freezing.
It is snowing.
Although in English these verbs do have what seems to be a subject, it, it is arguably completely devoid of semantic meaning and merely a syntactic placeholder, a dummy subject. Contrary views of this use of it do exist, however, making it here potentially a "quasi-(verb) argument" or simply a normal subject.
Avalency is more clearly demonstrated in pro-drop languages such as Spanish, which do not grammatically require a dummy pronoun as English does. For instance, the Spanish equivalent of it's raining is llueve.