Purchase-money second liens are exactly what you would expect, given their name: they are second liens that are taken out for the purchase of a property.  They are usually done as a way to avoid private mortgage insurance (PMI) and always carry with them a higher interest rate than that of a first lien.  However, even with the higher interest rate, it almost always makes sense to take a second lien instead of PMI because your total housing payment is almost always less with a second lien.  AND, second-lien interest is tax deductible, just like first-lien interest. 

So, you ask, why would anyone want PMI when you can save money with a second lien? Well, good question! The only problem with second liens is that they are becoming increasingly difficult to qualify for, especially if you are a first-time home buyer.  One other problem is that they typically are balloon mortgages that are due in 15 years, which makes some people nervous.