Fútbol vs. balompié
The words 'fútbol' and 'balompié' are both used in Spanish to refer to the sport known as 'football' or 'soccer'. Generally, their meanings are interchangeable, but there are subtle differences based on regions, preference, and historical use.
Fútbol
This is the most widespread term used to refer to the game of football (or soccer) in Spanish-speaking countries. The word is a direct adaptation of the English word 'football'.
Me gusta jugar al fútbol los fines de semana.
(I like playing football on weekends.)
Balompié
This word also refers to the game of football or soccer, but it's less commonly used. It's more of an old-fashioned term, and it originates from combining the words for 'ball' (balón) and 'foot' (pie). Some people prefer this term as a more 'Spanish' alternative to the anglicized 'fútbol'.
El balompié es un deporte que requiere gran habilidad y resistencia.
(Soccer is a sport that requires great skill and endurance.)
Summary
'Fútbol' and 'balompié' both refer to the sport known internationally as football or soccer. While they mean essentially the same thing, usage may depend on context and nuance. 'Fútbol' is more universally understood and used, while 'balompié' has a more Spanish flavor but might not be recognized by all Spanish speakers.