Sixteen pulses on two wires

What a servo asks for

A hobby servo has three wires: ground, power, and a signal. On the signal wire it expects a pulse about every 20 ms, 50 times a second. The width of that pulse, somewhere near 1 to 2 ms, is the position. Stop the pulses and the servo stops being told where to be.

A microcontroller can make that pulse on one pin with a hardware timer. Sixteen servos need sixteen pins and sixteen timer channels, all running at once, and a sketch that never blocks them.

Handing the pulses to a chip

The PCA9685 is a chip that keeps sixteen PWM outputs running from its own oscillator. The microcontroller writes each channel's pulse width into the chip once, over I²C, and then does something else. The pulses continue, unchanged, until it writes a new width.

So the traffic on the two wires is only the changes. A servo that holds still costs the bus nothing, and the sixteen pulse trains never jitter because the sketch was busy.

Two wires, and the two they need

I²C is two signal lines, SDA (data) and SCL (clock), plus a shared ground. The board also needs VCC, the supply for the chip itself. Those four wires are all a microcontroller gives it.

Every board on the same two wires needs its own address. Six solder pads on the underside set it, and the datasheet counts 62 usable addresses, so one pair of pins can reach far more than sixteen servos.

What the chip does not do

It does not power the servos. Their current comes from a separate supply on the board's V+ rail, and that split is the most important thing in this book: V+ and VCC.

It does not know about angles either. It sends pulse widths, and which width means which angle is up to each servo: A pulse, not an angle.