You can disregard that unhelpful post from Bluejets. Bluejets, it's not necessary to try to answer every post - only answering the ones you know about is fine!
The "number of bits" tells you something about the complexity and processing power of the processor core. It is the native "word size" of the device, i.e. the width of the binary numbers that it is designed to process naturally and efficiently. Small micros are typically 8-bit. The CPU in your PC is 32-bit or 64-bit.
Eight-bit micros normally have I/O ports that are eight bits wide as well, for convenience. Sometimes, one or more ports are not fully brought out to the device's pins. This will happen if the number of pins available for I/O is not an exact multiple of the port width; at least one of the ports may be only partly implemented.
If an 8-bit port is fully implemented in the device and brought out to eight I/O pins, and if all of those pins are "set to output mode", i.e. they are all under control of the micro, then the micro can produce 256 different combinations of output values. Each line can be either high or low, i.e. one of two states. 28 is 256.
Often though, port pins are used for discrete individual control signals, so one pin might control part of one circuit, two more pins might control part of a different circuit, and so on. In those cases it's not useful to point out that there are 256 possible output state combinations.
Also, ports are used for both input (allowing the firmware to detect the state of parts of the circuit) and output (allowing the firmware to control parts of the circuit), and often, ports are split between those functions. For example a port may be used as five inputs and three outputs. It depends on the requirements of the system and the capabilities of the port pins.
Certain port pins also have dual functions with built-in peripherals, such as ADCs, timers, PWM generators, etc. For each pin, firmware decides whether the pin will be used as general purpose I/O (GPIO), i.e. a simple digital input or output through a port, or whether it will be used for a special function, such as an analogue input, a clock input, a PWM output, or whatever.
PWM uses a single digital output pin to produce an analogue signal. The pin is only ever either high or low - it is a standard digital output pin - but it alternates between high and low at a fairly high frequency, called the PWM frequency. The duty cycle of the PWM pin varies according to a value programed into the PWM generator inside the device, and the signal from the pin is passed through some simple analogue filtering (just a resistor in series, then a capacitor to ground, sometimes repeated) to "smooth out" the PWM frequency and give a voltage that corresponds to the duty cycle of the signal.
This analogue signal can then be used to control the circuitry. PWM is a cheap and relatively low-performance way to provide a crude analogue output from a device whose pins are only capable of digital output.
A bit of Googling will tell you all about how PWM works, and check out that last link in Bluejets's post.
