In a paraphrase, you are taking someone else's ideas and thoughts and putting them into your own words. This does not make the paraphrase your own work! When paraphrasing, make sure to:
A paraphrase is NOT breaking out the thesaurus and replacing words from the original source with synonyms. Paraphrases are actually demanding to write; you want to capture the essence of the original idea, but the wording and sentence structure are fundamentally different.
Original: The dog jumped over the cat.
Bad paraphrase: The canine hopped over the feline.
Why? This is plagiarism. The sentence structure is exactly the same, with words substituted.
Good paraphrase: Because the cat was in its way, the dog had to make a running leap.
Why? It reflects the meaning of the original, but shows the author thought about it for a little bit.
Remember that paraphrases need to be cited!
Unlike a quote, in which you are repeating someone else's words, paraphrasing allows you to retain your own voice in your narrative. Paraphrasing shows a deeper level of understanding about the original source than quoting does.
The OWL at Purdue site has some paraphrasing exercises to help you learn this essential skill.