As previous posts have pointed out, it was certainly a turning point because it allowed for escalated action and participation in the war by US forces.
It is also a very interesting piece of history if you look at the actions on August 4 and the alleged second attack that is heavily disputed and that lacks any physical evidence. It certainly wasn't the first time that an attack or incident has been blown out of proportion, but the blatant nature of it is an interesting starting point for a lot of discussion and investigation.
I tend to agree with brettd in that Johnson was looking for a way to increase the involvement in Vietnam. By allowing the Maddox to patrol that close to North Vietnam he was most definitely daring the North Vietnamese to do something. Once they did the US really had no choice but to increase involvement.
One can pretty reasonably ask what American warships were doing patrolling so close to North Vietnam at the time anyway. This leads me to believe that LBJ had pretty much already decided he wanted to escalate our involvement in the war, knew he would have to get Congress on board at some point, and needed a provocation to do so. The Tonkin Gulf Resolution passed 504 - 3, so I'd say the plan worked.
The standard belief at the time of the attack on the Mattox was that the attack was unprovoked. There is now some argument that the Mattox had put itself into a position of jeopardy. Prior to this time, U.S. troops in Vietnam were acting as "advisors." They saw some combat action; but it was played down, as there was no support at home for a full scale war. The Mattox attack created such furor at home that Congress passed the resolution authorizing the President to take "all necessary action" to protect United States troops. By so doing, Congress virtually abdicated to the President the right to wage war on his own volition. Presidnet Johnson followed through committing large scale troops; although he was himself somewhat misled from field reports he received from General Westmoreland that the U.S. was "winning."
This is a turning point because this event led to the major escalation of US involvement in the Vietnam War. Before the incident, the US was only involved in Vietnam in a relatively small way and Congress had not authorized any large-scale involvement. After the incident, Pres. Johnson got Congress to pass the Gulf of Tonkin Resolution that gave him and future presidents the power to take any military actions they deemed necessary in Vietnam.
Therefore, the incident was a turning point because it led to "unlimited" American involvement in Vietnam, not just to some small ramping up of the US presence.