The quote you mention is spoken by Jack Merridew in chapter three of Lord of the Flies, by William Golding. Jack has just returned to the beach after another unsuccessful pig-hunting expedition. He is frustrated by that, and Ralph is frustrated because he is working virtually alone to make shelters for everyone. With the exception of Simon, the others '"work for five minutes, then wander off or go hunting." All Jack can think about is better ways to hunt.

Their conversation centers around the need for shelters because the boys are all sleeping restlessly and experiencing nightmares because they are afraid of what they call "beasties"--the non-specific term for everything the boys fear. Even Jack and Ralph tacitly admit to some fear, as in this statement by Jack:

—in the forest. I mean when you’re hunting, not when you’re getting fruit, of course, but when you’re on your own—” He paused for a moment, not sure if Ralph would take him seriously.

“Go on.”

“If you’re hunting sometimes you catch yourself feeling as if—” He flushed suddenly. “There’s nothing in it of course. Just a feeling. But you can feel as if you’re not hunting, but—being hunted, as if  something’s behind you all the time in the jungle.”

Ralph is "incredulous" and Jack quickly tries to pretend he has not really revealed some of his own fears, but it is too late. Neither of the boys is interested in talking about their own fears, so they quickly change the subject.

This admission of fear is real and both boys understand it; however, they decide not to talk too much about it so their fears will not overcome them as they have some of the littluns. 

In *Lord of the Flies*, what does Jack mean by feeling hunted while hunting?

I would like to make a small correction to the question. The quote provided is not quite right. The quote can be found in chapter 3 and is spoken by Jack. The following is the full quote.

But you can feel as if you're not hunting, but -- being hunted, as if something's behind you all the time in the jungle."

This is an awesome quote in this book, and it is made especially awesome because it is Jack that says the quote. This is a rare moment of vulnerability being expressed by Jack. He typically presents himself as strong, brave, and violent. He's a hunter, but here we see him admitting that he has fears and that there isn't something quite right about the island. He is echoing Ralph's previous statement a moment ago that somehow the island isn't a "good" island. That's important if "good" is carrying a moral value to it. If the island isn't good, then it is evil. Jack realizes that he might not be the alpha predator/hunter on the island. He verbally expresses that something evil might be hunting all of them. It could be a beastie, or it could be their general descent into savagery.

This has meaning on two levels.

First, literally, Jack is having that feeling that we all feel in the dark when we can't tell if someone else is there. We almost believe there is someone because we have fear of the unknown. This may mean that while Jack's hunting, he is actually feeling the presence of the pigs who are escaping his line of sight.

Second, figuratively, Jack is feeling the evil of the place. Many different literature texts refer to evil as something tangible. In fact, "The Most Dangerous Game" is also set in a thick jungle on an island. Most Puritan literature references the evil that lives in the forest. These unchartered places were considered the residence of evil. Eventually in Lord of the Flies we see this belief come to fruition because the kids are influenced by the evil and begin having no concern for human life. Likewise, they give evil a vessel in the pig's head that they place on a stick as a symbol. The darkness and evil could be that which is the "something behind you" that Jack references.