POWER SUPPLY

I think you have to read the User Manual for your discovery board together with the Data Sheet and Reference Manual for your stm32f407 to get the best explanation.

But if, having read the appropriate parts of those, you are still having difficulties please let us know which bits you don't understand and we might be able to clarify them.

What is your technical level / experience / understanding (to know what level our answers should be written at)?

For example, we could imagine from you question that you have just acquired one of these boards, want to power it up to play with it (the best way to learn) but aren't sure how to apply power. The User Manual goes through this, much more clearly than I could.

Help us to help you,

Danish

I agree with Danish, check the user manual.

As a short explanation, VSS/VDD are the power supply pins of the MCU.

VBAT is a special input for connecting a battery, usually to retain the RTC and a few registers. The board/MCU works fine without any battery.

Not sure what you mean with voltage regulators, but they "translate" the external supply (usually 5V from USB or another supply) to the 3.3V the MCU is supplied with (VSS/VDD).