The U.S. State Department defines terrorism as: "premeditated, politically motivated violence perpetrated against noncombatant targets by subnational groups or clandestine agents, usually intended to influence an audience." Under that definition, Palestinian attacks on civilians inside Israel would be considered terrorism; so would lethal attacks on Palestinian marketplaces by Israeli settlers in Hebron or elsewhere. Palestinian attacks on Israeli soldiers, military checkpoints or other military targets would not fall under the definition of "terrorism," although many U.S. politicians and pundits describe them as such.
The vast majority of Palestinians have never participated in any armed attack against anyone. Many, perhaps most, Palestinians are opposed to attacks on civilians anywhere, and many are opposed to any attacks inside of Israel. In the spring of 2002 a large group of well-known Palestinian intellectuals signed a public statement condemning suicide bombings against civilians. But virtually all Palestinians understand the desperation and hopelessness that fuel the rage of suicide bombers and their increasing (and ever-younger) followers.
Throughout late 2002 and the first half of 2003 as the second intifada ground on, Israeli assassination attempts, often with large numbers of "collateral" deaths of bystanders, many of them children, escalated. In response, so did Palestinian attacks on military targets in the occupied territories and also on civilians inside Israel. While many, perhaps most, Palestinians understood the rationale behind those attacks, they also recognized how the brutality of attacking civilians brutalized their own society as well, while pushing Israeli public opinion further and further to the right.