The Spanish word 'anfitrión' (meaning 'host') comes from the Greek name 'Amphitryon' (Ἀμφιτρύων), who was a mythological king of Tiryns. The name Amphitryon itself is composed of two Greek elements: 'amphi' (ἀμφί) meaning 'on both sides' and 'tryo' (τρύω) meaning 'to wear out or exhaust'. The word evolved to take on the meaning of 'host' based on a famous story from Greek mythology where Amphitryon was known for his hospitality, particularly in a tale where Zeus impersonated him to visit his wife Alcmene. This story was later popularized in various literary works, leading to the name becoming synonymous with someone who hosts or entertains guests.

The prefix 'anfi-' appears in other Spanish words like 'anfiteatro' (amphitheater) and 'anfibio' (amphibian), all derived from the same Greek root 'amphi-' meaning 'on both sides' or 'around'. These words might be more familiar to beginning Spanish learners and can help remember that 'anfitrión' has something to do with surrounding or encompassing others, as a host does with their guests.

English speakers can relate 'anfitrión' to several English words that share the Greek 'amphi-' prefix, such as 'amphitheater' and 'amphibian'. While these words don't mean 'host', understanding that they all come from a root meaning 'on both sides' or 'around' can help remember the Spanish word - just as an amphitheater surrounds its audience, an 'anfitrión' surrounds their guests with hospitality.