As was mentioned in the previous posts, Piggy makes this statement during an assembly meeting in Chapter 5 when the boys begin to discuss the identity of the beast. Ralph initially states that there is no such thing as the beast on the island, and Jack agrees with Ralph's assessment of the situation. Piggy then takes the conch and attempts to solve the problem of the beast pragmatically. Piggy mentions that he understands there is such a thing as fear inside people's minds, but he also believes that "life is scientific." He then says he believes that there is nothing tangible that the boys should fear on the island unless they begin to fear other people. Piggy's statement reveals that he is aware of man's inherent wickedness and believes that the boys should fear one another. Even though a beast does not physically exist on the island, the inherent evil in each boy is something real that they should recognize and fear. Essentially, each boy on the island has the capability of committing barbaric acts that can harm others.
This is a statement regarding projection. Piggy understands that there is no need for a physical beast or monster on the island to create an "objective" fear among the boys, something which they reasonably should fear because the danger that the boys represent to themselves is (or can be) quite real.
These words are spoken by Piggy, the logical, scientific thinker. In Chapter Five he approaches the understanding that the beast lies within the hearts of man as he suggests "unless we get frightened of people." But, the boys do not understand him and they heckle him instead. In their ignorance of the inherent evil of mankind, the boys fear something external; when Simon attempts later to explain what he understands intuitively, the hunters savagely kill him, proving the truth of Simon's comprehension of evil.
The true beast is the fear within the boys and for one another. There is no tangible beast in the animal sense--only the fears inside their own hearts and the fear of the breakdown of civilized behavior.