'To throw up' is a phrasal verb that has a number of idiomatic meanings in English. Of course, it is also used literally, to mean that something is thrown up into the air, or thrown up out of the sea onto the beach. The more common idiomatic usages include:
- Most often, 'throw up' is used to mean 'to vomit'. This is still considered slang by many dictionaries, although it has been around since at least 1732. 'Vomit' has been around since the 1400s and comes from Latin, so it is understandable that medical professionals prefer the term 'vomit', but 'throw up' is a well-established euphemism, and is commonly used in informal contexts.
- It can also mean to construct or put up quickly, as in 'to throw up a tent'. This implies a rather slapdash process, and is more like to be used when talking about temporary or shoddy constructions. This sense can also be used to refer to very minor assemblies ("she threw up a projection screen").
- Occasionally it can also be used to mean 'to produce', as in "the election process always throws up a few surprises".
- Less frequently it can mean to give up or relinquish, as in "he threw up the mayoral race as a bad job". This is perhaps more common in the past, but is rarely used these days.
- It is worth noting one commonly used variation of the literal usage of the phrase; 'to throw up one's hands' means to raise one's hands quickly, generally in resignation, surprise, frustration, or self-defense. One might also throw up one's arms.
'Throw-up', with a hyphen, is an informal usage that does not appear in traditional dictionaries. It may be used informally as a noun meaning something that was created or put up quickly, most specifically graffiti. You can find more in that node.