My parents signed over a piece of land to me last year which was an inheritance from my grandparents estate (they've been gone for a while). I'm in the process of selling the property for $120K and am purchasing another property (in a different county) for $105K? What will my capital gains obligation be calculated on... $120K, $15K?

Does it make a difference if it was a gift rather than an inheritance (i.e. I'm not exactly sure if it was gifted to me prior to death or I inherited it after death. The property has been under my parents' name? Thanks.

Your parents inherited the land. They don't pay any inheritance tax. Also the cost basis of the property to your parents is the Fair Market Value (FMV) of the property at the date of death of your grandparent. Read more about inheritance: Your U.S. Tax Return: Tax on Inheritances

Your parents signed over a piece of land to you --- this is a gift. The person who receives a gift does not pay any tax. But your parents must file gift tax return. What is your cost basis depends both on the FMV of the property at the date of gift and your parents' cost basis.
Read more about gift tax: Your U.S. Tax Return: The U.S. Gift Tax

Now when you sell the property at 120K, you must report the sale on schedule D and figure out your profit based on the cost basis.
After that what you do with the money is your business. It does not change your profit or loss.