The mortgage balance is meaningless, for tax purposes.
The cost basis in a gift is the giver's basis. Your cost basis in the house will be what your mother paid for it*. So, when you sell the house, your taxable capital gain will be the difference between what you sell it for and your cost basis**.
*You would add any improvements, you mother made over the years, to the cost basis. If you father is deceased and previously owned the home with your mother, there is another cost basis adjustment that is made for when the titled transferred solely to her.
**The usual rule, for a gift, is that the recipient's basis is the giver's basis (what you mother paid for it). But there is an exception for the gift of her home, where she retained the right to live there ("life estate"). (see
http://www.njelderlawestateplanning.com/2010/02/articles/estate-and-inheritance-tax/life-estates-est... which states in part "If you give away an asset and keep a life estate in that asset..... the cost basis of the house is "stepped-up" to the value of the house on date of death [IRC 2036]")
The difference between the current value of the house and her cost basis is a gift of equity. If the total value of the gift (basis + equity) is more than $14,000, you mother (not you) will need to file a gift tax return (a separate filing from income tax). "Gift Tax" is somewhat of a misnomer. Even though a gift tax return may be required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See
https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...
