Can someone explain what each pin does on an LM3914 dot/bar graph chip?
Generally the pins of an IC fall into four types and are pretty self explanatory:

(1) Power (where you connect the power supply)

(2) Input (where external signal go in)

(3) Output (where signals come out)

(4) Control (where you set the IC to do something e.g. reset)

You sometimes come across a pin marked NC - this means Not Connected so you don't have to worry about it. Here's a typical LM3914 circuit.

 

The POWER PINS are 2 (0V) and 3 (+12V)

The INPUT PIN is 5 (variable voltage input)

The OUTPUT PINS are 1, 18,17,16,15,14,13,12,11,10 (10 sink outputs)

This just leaves the CONTROL PINS. (4,6,7,8,9)

Pin 6 (Rhi) and Pin 4 (Rlo) are connected to the HI and LO ends of an internal resistor network (10 x 1K0) which produces a reference voltage on each comparator input. In this circuit pin 6 is connected to the +12V supply through R1 (100k variable) which controls the range of input voltage. To complete this comparator ladder pin 4 is connected to ground.

Pin 7 is an internal voltage reference out. (1.25V) Pin 8 is a reference voltage adjustment. By connecting pin 8 to ground the output at pin 7 will be 1.25V. The load resistance put on pin 7 will control the LED brightness - hence a 1K0 (R2) is connected to ground.

Pin 9 controls the mode of display (bar or single LED) (see data sheet for full explanation page 9/10 http://www.ti.com/lit/ds/symlink/lm3914.pdf)