Me encantaría (ir al cine) means I would love to (go to the movies). Literally, “It would enchant me (to go to the movies)” or “Going to the movies would enchant me”. The subject of this sentence is ir al cine, and when an infinitive such as ir is used as a subject, it is considered singular; therefore, the main verb, encantaría, has a singular conjugation. Note the difference between Me encanta and me encantaría.
Me encanta ver películas (I love watching movies/I love to watch movies).
Me encantaría ver una película (I would love to watch a movie).