I believe MTD meant opposing directions. BF3 takes on a trigonal planar shape. So the central atom is B and the 3 F atoms are bound to B on the same plane. It's very difficult to explain through text without any visual aid, but I will try my best.
First, imagine that you have two atoms, lets say X, attached to a central atom, A (AX2). The molecule will take on a linear shape (X-A-X). Let's say that X is the more electronegative atom of the two. Each bond has a dipole moment pointing toward X. Because each bond is exactly opposite of each other (180 degrees), they will cancel each other out.
Now, add another X atom to the molecule (AX3). The 3rd X atom will come in from the top of the molecule and attach itself to the central atom, A. The addition of the 3rd X atom pushes on, or repels, the other 2 X atoms. The molecule as a whole has shifted from the linear arrangement to a flat trigonal planar arrangement with 120 degrees between each X atom.
Each bond will still have the same magnitude of dipole moment. The two X atoms at the bottom can be thought of as vectors. They both point down, but one is to the left and one is to the right. If you add this up, the left and right will cancel each other out and the net dipole moment will be pointing downward. This downward dipole moment is cancelled out by the 3rd X atom, which has a net dipole moment pointing upward.
Does that make sense?