C'è is the contraction of ci è (it's never used this way, though) and it translates there is.
Ce n'è is the contraction of ce ne è (its contracted form is preferred in everyday use; on the written page you're more likely to find the full form, especially in formal writing). That ne is a little word that replaces "of it/them" in conversations like:
C'è del burro? Is there butter?
Sì, ce n'è. Yes, there is [of it].
Quanto ce n'è? How much is there [of it]?
Ce n'è molto. There is much [of it].
Hai delle caramelle? Do you have (any) candies?
Sì, ce ne ho. Yes, I have [of them].
Ci sono delle caramelle? Are there (any) candies?
Sì, ce ne sono. Yes, there are [of them].
Ne is basically used to refer to something previously addressed.
Quanti anni ha il sindaco? How old is the mayor?
Che ne so! "What do I know [of how old the mayor is]?" (How could I know!)
Ce, in these cases, means the same as the ci in ci è (c'è), meaning "there, in that place". Ce is basically ci undergoing a vowel shift in the presence of ne, la, li, lo, le.
Hope this helps! :)