I don't mean offensively in the term that you are giving people the bird, or cutting people off. The term refers to moving forward in relation to surrounding traffic. Many motorcyclists believe this is safer than riding defensively. I feel it depends on the situation.
However, there are certain instances where moving forward through traffic will allow for more focus on what's ahead of you, instead of worrying about traffic behind you. Keep in mind you still want to maintain your space cushions and distances from surrounding traffic and hazards, all the while moving steadily forward ahead of the pace of traffic, so you can concentrate on what's going on ahead of you. That does not mean, you don't have to check your mirrors every once in a while to see what's going on, and be aware of your surroundings.
Another important aspect of riding offensively is lane protection. The entire width of the lane is something that you need to utilize as a motorcyclist. Make sure you position yourself to keep other cars and motorists, and making it too enticing for them to drift over into your lane.
Lane positioning is an important part of riding offensively, and when done right, can help keep you safer, and maintain distances from surrounding traffic.