I guess it may be a combination of two things
1. It keeps the weather off the lower walls/foundations.
2. The distribution of weight in the higher floors stops the lower walls from spreading outwards.
I think it's called jettying, and I've always assumed it was to provide increased floor space in increasingly crowded towns, but I think both of Rick's reasons also sound valid.
You see examples of double jettying too, with the next floor projecting further again, to the extent that the upper floors of buildings on either side of narrow medieval streets like The Shambles in York are near enough together for people to shake hands across the gap.
Until the invention of and common use of the iron girder, it was only the half timbered houses that could be built this way with any sort of ease. It isn't found all that much outside towns, so efficient land use can be a factor, and as a lot of the town centre buildings were used for trade as well as living in, it would provide extra cover for goods on display and customers as well.
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