Let's say the bank holds 100 dollars in deposits.
If they are required to hold 5% in equity (or any other asset class that contributes to the requirement), then they can loan out 95 dollars of the 100 dollars.
If they are required to hold 20% in equity (or any other asset class that contributes to the requirement), then they can only loan out 80 dollars of the 100 dollars.
A relevant concept is "risk-weighted assets", where a highly rated asset (lower risk) contributes more to the requirement than a lowly rated asset (higher risk). If you read up on Basel III in Wikipedia, you can find out more about different types of capital requirements and other stuff that goes with that, in addition to other relevant concepts such as liquidity requirements, etc.
Sometimes the main idea is to prevent a minor run on the bank from turning to catastrophe (maybe a depositor takes their 10 dollars out of the bank, and the bank is left with minus 5 dollars, and cannot meet the ongoing financing requirements of an investment project that they had previously committed to). Other times, it may prevent a small economic downturn from causing havoc in the financial system (maybe several loans are not repaid until later, and the bank has no additional liquidity to finance any new investment projects, causing investment in the economy to collapse). In both cases, the higher capital requirement provides protection against a small problem with one or two banks turning into an economy-wide catastrophe (although it is possible for the requirement to be "too high".)
In other cases, a central bank may use capital requirements to influence overall credit in the financial system, similar to how central banks manage interest rates to influence inflation and thereby other macro variables.