Form 1099-G reports certain types of government payments you received during the tax year. Examples include unemployment, paid family leave, or if you received a state or local tax refund for a prior tax year.
Many types of 1099-G income are taxable, including unemployment, although it is your total income (from all sources) that determines whether or not you need to pay taxes on 1099-G payments. More info.
The 1099-G is also used to report less common sources of income, including taxable energy grants, agricultural payments, and others.
If you did not get a 1099-G but received unemployment pay, go here.