Explaining "Subject-To" to a seller

[Josh Stevens]

I am trying to make a deal work for me to buy a small apartment building.  I really don't think that I can make this a deal if I try to get a commercial loan.  I threw the term "Subject-To" out there and the seller wasn't familiar with it, but she did ask if I wanted her to approach her lender about me assuming the current loan.  I figured, why not.  That route may be extremely unlikely to take, so I would like to further explain "Sub-To" to the seller to see if she is interested.  I've investigated it on BP to make sure I understand it better, but I would like to approach her in a very professional and non-shady manner so that she knows her interests are covered. 

Is there a good way to clearly explain the approach that will show that it is a legitimate method of sale?