Budget Constraint
  
Budget constraint is a fancy econ term for that feeling you get when it's your turn to pay for a round of drinks...and when the bartender says the amount you owe, you suddenly realize that you'll be eating Ramen noodles until your next paycheck.
Basically, budget constraint is the amount of stuff you can buy with the amount of money you have at your disposal ("stuff" in this case being a broad term that includes both goods and services...a haircut would be "stuff" in this reckoning).
By formalizing this relatively obvious concept, economists can start to think more deeply about consumer spending. For instance, you can change a person's budget constraint in two ways. You can change their income (if they get a raise, now they have more in the budget). Or you can change prices (if the price of stuff...like that haircut...gets cheaper, they can buy more of it, even though they have the same nominal amount of money).
Economists being economists, they like to graph things like budget constraint in mathematical terms, turning that "I just paid what for six tequila shots and a rum and Coke!?" feeling...into cold equations.