Both "или" and "либо" mean "or" in Russian (or when used in succesion, "either...or"). There is hardly any difference in meaning between the two words. That being said, there is a nuanced difference in their usage.
"Или" vs. "либо" nuance
"Или" is a complete equivalent of "or" in English and is extremely common.
"Либо" is used in more old-fashioned, archaic text, and is much less common. The word has a slight difference in use, where it means "or" as in "one or the other." "Либо" excludes the other option, while "или" does not.
Example sentences with "или" and "либо"
- Добро пожаловать! Хочешь чай или кофе? = Welcome! Would you like tea or coffee?
- Мы можем встреться либо в понедельник либо в среду. = We can meet either on Monday or Wednesday.
- Или пан или пропал. = Sink or swim (expression).
- Либо да, либо нет. = Take it or leave it (expression).
- Или ты забыл или ты не знал. = Either you forgot or you didn't know.
- Либо лекарство, либо нет. = Either there is a cure or there isn't.
- Какую таблетку ты выберешь красную или синюю? = Which pill would you choose, red or blue?