Can someone explain what each pin does on an LM3914 dot/bar graph chip?
I think the picture on page 8 of the data sheet, and the text starting from page 9, explains it about as clearly as anyone can make it. I hope you didn't stop reading it after seeing those cryptic graphs?

In short: there's not much more to it than a pin to set the LED brightness, a pin to select between dot and bar mode, a pin for the input voltage to be measured, and the pins for the LEDs and the power supply.