If your mother gives you her house and then you sell it; you will have to report a long term capital gain (LTCG)* of $175,000 (300K - 125K = 175K). Depending on how much total income you have LTCG are partially taxed at 0%, 15%, 20% and/or 23.8%.
If your mother sells the home, herself, there is no tax. Taxpayers may exclude up to $250,000 of gain on the sale of their principal residence if certain rules are met.
*It's considered a long term gain, because your mother's holding period transfers to you with the gift.
