It first generates an offset value in ESI: 15 if the value to divide was negative, or 0 if it was positive.
Then it adds this to the original value. This is the cunning part - well I think so anyway. It ensures that for the values where x>>4 would give the wrong value (i.e., -15<=x<0), x is made positive and smaller than 16, so that x>>4 gives the correct value of zero. For all other values, the bottom 4 bits don't affect the result of the division, so it's fine to offset them as well.
(Don't think I've ever seen VC++ generate anything like this, but I'd pretty much always have an explicit shift rather than a divide by 16 so maybe it does and I'd just never noticed. The choice of 16 usually comes from having some 4-bit field somewhere, and when dealing with bitfields you're best off using bitwise instructions.)