Ellipsis simply means "omission". In punctuation, three dots means something is missing from the sentence ("...and so on...") An elliptical conversation is one where a lot of key information is left out because the speakers know it already ("Have you got one?" is elliptical - it assumes that you know what "one" means.)
In grammar, it's basically the same; we leave out the words (in spoken, informal English) that our hearers are sure to infer from the context:
-Got any money? ("Have you" is omitted)
-Must go. ("I")
-There's something missing, but I don't know what. ("It is.")
-I've brought the documents, as agreed. ("We agreed.")
-I carried the bag and my friend the suitcase. (In leaving out the second "carried", you can create confusion here - do you mean that the suitcase is your friend and you carried both him and the bag?? This is an example of why ellipsis must be used with care.)
In grammar, it's basically the same; we leave out the words (in spoken, informal English) that our hearers are sure to infer from the context:
-Got any money? ("Have you" is omitted)
-Must go. ("I")
-There's something missing, but I don't know what. ("It is.")
-I've brought the documents, as agreed. ("We agreed.")
-I carried the bag and my friend the suitcase. (In leaving out the second "carried", you can create confusion here - do you mean that the suitcase is your friend and you carried both him and the bag?? This is an example of why ellipsis must be used with care.)