NH$_3$ has a trigonal pyramidal shape with a lone pair on nitrogen. The dipole moment of the three N–H bonds and the lone pair add constructively.
NF$_3$ also has a trigonal pyramidal shape, but the highly electronegative F atoms pull electron density away from N, opposing the dipole due to the lone pair.
As a result, NH$_3$ has a higher net dipole moment than NF$_3$.