Traditionally, it is considered neither, though it is sometimes called a mood for lack of a better word. The word function would seem the best term. I am assuming that you are talking about the word would in your example. The adjective "conditional" just means "related to a condition"; when used as a noun, it usually refers to a function of the past subjunctive tense of modal verbs (would, could, might, and should).
There are three traditional moods in English, indicative, subjunctive, and imperative; there are several tenses, which are combinations of moods, aspects, and temporal properties (you might say past and present are aspects, though they are usually not so called).
There are three types of conditional sentences, as Henry has pointed out, which are mainly just sentences in which an explicit or implicit condition is present. There is a function of the past subjunctive that is called conditional because it is used with one of these types, the so-called hypothetical condition (if he were rich, he would be unhappy). I think that is the one you mean; while it is sometimes called a mood, I find this unclear and confusing: how can something be of two moods, both subjunctive and conditional? Function is the term that both fits best with established terminology and best describes what kind of phenomenon it is.