The word swell can be used as an adjective and also as a noun and verb. When you are using the word as a verb it is usually used in association with 'up' and the phenomenon that you can figure out from the term 'swell up' is to become bigger and more round. The sentence that can help you in understanding the word well is given below: His arm is beginning to swell up because a bee has stung him. The word can also be used in the figurative context and you can use the word to convey the idea of something that is increasing in size.
As an adjective the word is used for something that is very good and enjoyable and when you are using the word as a noun it conveys the idea of the movement of the sea when the waves are getting up and down without any break. The noun form also conveys the same idea as that of the verb one.