Paraphrase is stating someone else's ideas in your own words. If you think about it a little, you will realize that it's something that we all do, all the time. You watch the NBA finals on TV, you tell me the story of how Malone fell short and Jordan was a hero again, and I retell the story to my friend in my own way. I probably don't stop to give you credit. If we were constantly stopping to give credit, then our discourse would bog down. However, since we are having a conversation, if you need to know more, you can ask me: What's the source of that stuff, man? And I can say: it was Jimmy, he watched the game so he should know. And you say: Jimmy is an idiot, and I say... well, so it goes.
So why do you have to cite the source of something when you are writing. Doesn't this also bog down the discourse? Yeah, in some of the papers you read it seems like there are more footnotes than the paper text itself. But yes, you do have to cite sources, even for paraphrase. You see when your friend reads your paper, you're not around. He can't call you and ask you for the source. You may not remember unless you put in the citation anyway (then you have really left yourself vulnerable if a professor does know the source, as he or she probably will).
So when you are writing the paper, think about the reader and what questions he or she would ask. If you can imagine the reader saying: "what was the source of that idea?" then you should cite it, even if you rewrote it in your own words.
Let's paraphrase that Heilbroner passage.
The population problem manifests itself not only in hunger, but also in the specter of urban breakdown that arises from large population growth. Unemployed people pour into depressed cities such as Calcutta, stretching both the cities and the people to the breaking point as they fail to find work. As population growth continues at a rapid pace, such places will become the very image of third-world debasement.
This passage must end with a citation of Heilbroner. I have captured all of the main ideas in his paragraph. Although I have used "my own" words, for example, substituting the idea of "pouring" into a city rather than "streaming" into it, and substituting the word "debasement" for "degradation," my argument tracks along with his. I am making the same argument. The fact that I changed some words and eliminated others does not mean that this is my own work.
This example illustrates a dangerous trap for the naive or not so naive. If you were to take the Heilbroner passage into a word processor, carefully edit out some words, rearrange the order of some others, and then use the thesaurus function to look up some good synonyms for other words (as I did for degradation), you might arrive at a passage like the one I wrote. You may think you are writing, but you are actually assembling. Even a passage that has been "sanitized" in this way, where the resemblance to the original comes only in the similarity of the arguments, you still must cite the original work.