Answer
Both pyrrole and furan have a lone pair of electrons in a p-orbital, this lone pair is extensively delocalized into the conjugated pi framework to create an aromatic 6 pi electron system.
Where pyrrole and furan significantly differ is that,
- in pyrrole there is an $\ce{N-H}$ bond lying in the plane of the ring and directed away from the ring
- whereas in furan, there is a full lone pair of electrons in roughly the same position.
The localized lone pair of electrons pointing away from the ring has a very significant effect on the dipole vector and is enough to cause the observed reversal in dipole moment direction between furan and pyrrole.
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