Paraphrase
To paraphrase something is, properly, to express the ideas of an original text in different words - without changing the meaning. (That is the verb; there is also a noun with the same meaning, a paraphrase.)
There has been a tendency recently to use the word paraphrase in a rather different sense: "to use the original words and apply them, with the necessary changes, to a different topic". This usage should be avoided in academic English.
A paraphrase in the proper sense of Shakespeare's famous line "To be or not to be" (Hamlet, III i 56) might read "Shall I or shall I not kill myself?". In the second, wrong, sense, a sports writer (for example) might say "To paraphrase Shakespeare's words, he cannot decide whether 'to be or not to be' an attacker or defender."
If you are tempted to use this wrong sense, think instead of phrases like "To adapt Shakespeare's words, ..." or "To misapply Shakespeare, ..." and so on.
Etymological note: The verb 'to paraphrase' comes, through Latin and French, from the Greek παραφράζειν (paraphrazein), which means 'to say the same thing in other words', being a compound of παρά (para, 'alongside', 'beside'; in compunds indicative of alteration or change) and φράζειν (phrazein, 'to show, tell, declare').