Does my girlfriend also owe estimated taxes? She owed both state and federal this year and paid. We don't quite understand what estimated taxes are.

We do not know enough about your GF's income to answer you.  You have not told us if she is a W-2 employee or if she is self-employed.  If she is a W-2 employee then perhaps the reason she owed is she did not have enough tax withheld from her paychecks throughout the year and she should change her W-4 at work to have more withheld from her pay to avoid owing.

https://www.irs.gov/newsroom/irs-withholding-calculator-can-help-workers-have-right-amount-of-tax-withheld-following-tax-law-changes

If she is an independent contractor (self-employed who gets paid in cash or receives a 1099Misc) then quite possibly she should be paying estimated quarterly taxes to avoid a penalty or a large tax bill at tax time.  Post back with more information and we can help.

Simple answer: if she will owe less than $1000 federal and $500 state (amount varies-check your state's requirement), she doe not need to do estimates.

 You should pay in quarterly estimated taxes if you don't have enough withholding taken out to cover the tax on all your income. 
You should make estimated tax payments for the current tax year if both of the following apply:
- 1. You expect to owe at least $1,000 in tax for the current tax year, after subtracting your withholding and credits. 
- 2. You expect your withholding and credits to be less than the smaller of: 90% of the tax to be shown on your current year’s tax return, or  100% of the tax shown on your prior year’s tax return. (Your prior year tax return must cover all 12 months.)