Wikipedia explains that a carbon budget (also called an emissions budget, emissions quota, or allowable emissions) is an upper limit of total carbon dioxide (CO2) emissions associated with remaining below a specific global average temperature. An emissions budget may also be associated with objectives for other related climate variables, such as radiative forcing.

So for example the UK carbon budget places a restriction on the total amount of greenhouse gases the UK can emit over a 5-year period.

The UK was the first country to set legally binding carbon budgets.

More information

UK Government Guidance on Carbon Budgets

Wikipedia article