A press is a defense (usually full court), where the defensive team put pressure on the offensive team and tries to get them to turn the ball over. The most common presses are a 1-2-1-1 (a diamond press) or a 1-2-2. Either way, the pressing teams usually tries to trap the person on the offensive team who the ball is in-bounded to. A half-court press can also be used where the press is the same, but the pressure does not start until the offense player get to the mid-court line. A press speeds up the tempo of the game and it's goal is to create turnovers which in turn result in easy baskets for the defensive team. A search of "diamond press" or "defensive press" on YouTube will reveal many videos that demonstrate what I am talking about.
It's when someone is dribbling and not past the mid line part on the court and if you are blocking them from coming down the court it's a press. Your team is suppose to be down the court already, so no one should be with the dribbler till he/she passes that mid-way line.