"We have never before seen a star moving fast enough to completely escape the confines of our Galaxy," says Warren Brown, part of the team at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts, who spotted the 700-kilometre-per-second star. Basically, why does just leaving the galaxy require a higher velocity than moving around within our corner of the galaxy, even though we are at the outer tip of the galaxy.
Not sure the following will help, but consider an electron in a metal. It moves with relative ease around inside of the metal, but it takes much more energy to escape. (Usualy called the "work function" of the metal.) When it was inside the metal the force (from other charges, but I will not mention that as I want you later to think "gravity force.") interaction with those in front of it (assume it had a little motion) is about the same as the force interaction with those behind. When the electron "breaks thru the surface" it feels only the attractive force (sometimes thought of as a single positive "image charge" located as if the surface were a mirror) pulling it back towards the interior of the metal. Now in your thoughts, replace the metal with the galaxy, the electron with the star, and electrical force with gravitational one. Another way to look at it is that the entire galaxy digs a deep "gravitational well" this poor star is trying to climb out of rather than just play arround with its friend inside the well.
I might be wrong, but here is my understanding. If something is moving slowly, it would not have the energy required to escape the gravitational field. As it moves toward the edge, it would gradually slow down, and fall back in (like throwing a rock into the air). Going back to the example, if the rock could be thrown really really fast, it would escape the earth's gravitation. Much like the star would escape the galaxy. If the star had a source of energy (like a rocket engine), that could keep it moving at the same speed, theoretically, it wouldn't have to move quickly at all. This is only theoretical becaue the energy source would add to it's mass, requiring more energy. So, if that helped any, it has to go fast enough so that it doesn't run out of energy before it escapes.
RubiksMaster, you have it right in post below, but no one should conclude from this that with even more energy the star (rocket ship, etc) could escape from the universe. There is no space "outside the edge of the universe." I don't know the latest ideas about this, but think this fact still widely accepted.
