You're meant to know about the effect that double bonds have on the shape of a molecule. The double bond pushes away the bonds with the hydrogen.
Now consider the centres of charge in your mind. One, where there is a double bond (highly negative) seperate from three positive hydrogens, and one when the bonds are evenly spaced out.
In BF3, the molecules are symetrical. What it means by this, is that they have the same angle between their bonds, and the importance of this is that the centre of positive and negative charge will be in the centre. The electronegative flourines, although apart from the nucleus, have their centre of charge in the nucleus (the centre of the molecule) because each of them has 120degrees between them.
In NH3, the positive hydrogens are pushed away by the highly negative double bond. As a result their centre of positive charge has now been moved away from the centre of negative charge.
As soon a the centres of charge are no longer on the same point, the molecule becomes a dipole.