A bit of this and a bit of that

Bit depth

Bit depth quantifies the amount of unique colours that are available in an image's colour palette in terms of the number of 0's and 1's, or "bits," which are used to determine each colour. This does not mean that the image necessarily uses all of these colours, but that it can instead specify colours with that level of precision. For a grey scale image, the bit depth quantifies how many unique shades are available. Images with higher bit depths can encode more shades or colours since there are more combinations of 0's and 1's available. 

Sampling - Sampling defines the number of samples per unit of time (usually seconds). Sample rate, how often these audio snapshots are taken is referred to as the sample rate. The more snapshots taken, the more detail the sound has. These pictures illustrate how sampling works:

Bits per pixel - Images are described as having a certain amount of bits per pixel, 1 bit, 8, bit, 24 bit, 32 bit etc. 

Putting this into disk space and file size:
1 byte = 8 bits, 
1 K byte = 1000 bytes, 
1 Megabyte = 1000 K bytes (1,000,000 bytes)
1 Gigabyte = 1000 Megabytes (1,000,000,000 bytes)
1 Terabyte = 1000 Gigabytes (1,000,000,000,000 bytes)

Think of a bit as one piece of information. Better described: one bit of information, an image is made up of many pixels, an image has a colour palette. If an image is a 24-bit image, then that image uses 24 bits of information to describe each pixel, (24 bits per pixel). The larger the bits per pixel, the more colours available in the palette.

Example: a 1-bit image has only two colors in the palette: black and white. A 24 bit image potentially has 16,777,216 colours in its palette.

Monochrome - Also called "mono." Refers to display screens that use one foreground and one background color; for example, black on white, white on black or green on black. The first terminals connected to mainframes and minicomputers were monochrome, and monochrome screens were widely used on early personal computers.

256 colours - 8-bit colour graphics is a method of storing image information in a computer's memory or in an image file, each pixel is represented by one 8-bit byte. The maximum number of colours that can be displayed at any one time is 256. There are two forms of 8-bit colour graphics. The most common uses a separate palette of 256 colours, where each of the 256 entries in the palette map to given red, green, and blue values. In most colour maps, each colour is usually chosen from a palette of 16,777,216 colours (24 bits: 8 red, 8 green, 8 blue).

Bit    7  6  5  4  3  2  1  0

Data   R  R  R  G  G  G  B  B

High colour/ true colour - 

Numbers of Colours:

The difference between Medium, High and Highest, over wise known as High color and True Colour is the number of numbers that can be used to represent the colour information for one pixel. Windows tends to use terms "Medium", "High" and "Highest" to represent the different alternatives, so I'll use that here:

Color Setting	Bits per pixel	# of different colors	Memory for 1280x800 screen
Medium	16	65,536	2 megabytes
High	24	16,777,216	3 megabytes
Highest	32(*)	1,073,741,824	4 megabytes

High colour or true colour ?

It depends on you, your vision, your monitor, your computer, your graphics card and how you use your computer. For most people these days we tend to land on 24 bit colour as the compromise. Pictures look good without going overboard, and the sky doesn't have that "stair step" feel in its colour gradient. If you know how your graphics hardware supports it, you might play with 32 bit as a speed enhancement, but in the long run it may not be worth it.