A budget is a plan on how you intend to spend your money. It takes into account all your incoming sources of money and all your expenses (required and discretionary). Sources of money will primarily comprise of your paycheck but could also include money from other sources such as investments or other efforts generating cash, such as a side hustle.
Expenses can be either required or discretionary. Required expense are items like rent, food, gas, insurance etc. These things must be paid to live a basic lifestyle. A budget will have to allocate money to these items first. Discretionary expenses are things that might seem important but are not truly necessary, such as eating out or entertainment. A budget should allocate for these items wherever possible.