If she gives it to you as cash (or a cash account) then there is no tax impact to you. Gifts you receive are not income to you and the federal gift tax is imposed on the person giving the gift, not the one receiving it. Your mother would need to file a federal gift tax return, but unless she's already used up her estate and gift tax unified credit (over $5 million) she won't have any gift tax to pay.
In addition to what TM says, mom may owe capital gains if to make the withdrawal caused stock to be sold above what her basis is on a non-restirement account. If it was a tax deferred (regular IRA, 401k) she owes income tax on it.
However, those higher figures only last until 2025, at which point they fall back down to $5 million (adjusted for inflation). It is right now unclear what will happen when the credit amount falls back down to that level for those who gave more than $5 million in taxable gifts during the 7 year period of the Trump tax act. Rather than go into a long discussion of that, I simply noted the $5 million figure as that will still remain good unless Congress actually changes the law.
Brokerage accounts are most often in stocks or other investments like bonds. If the money is in a money market fund, which is like it being in cash, then most likely your mother has paid tax on any interest income as it was earned, so there would not really be any tax impact. If its in stocks or other investments then you would either have a net capital gain or net capital loss. No one has any way to predict which way it would go. The capital gain/loss is the difference between your mother's basis in the investment (what she originally invested) and the amount that the individual investment sells for.