Analog and Digital Conversion/Analog vs Digital
What is a "signal", exactly? A signal in the sense that we will be considering in this book is changing value of electric voltage or current through a transmission medium. There are two general types of signals: periodic and aperiodic. Periodic signals repeat themselves after a certain period of time -- after they have cycled through one period, following periods don't contain any new information. Aperiodic signals, on the other hand, don't repeat themselves, and therefore can contain information. Signals also can be analog or digital signals, and we will discuss them both below.
Analog signals equate levels of electric voltage or current to amounts of information by applying some rule. Consider for instance, an analog clock, where the passage of time is displayed as the motion of the clock hands. In electric signals, a certain amount of voltage corresponds directly to a measured physical phenomenon. For instance, on an accelerometer, the amount of acceleration, measured in g's will correspond directly to volts. So at one g, we have 1 volt output, at 2 g's we have 2 volts output, etc. Analog signals have an advantage that they can represent any fractional quantity, by outputting an equivalent fractional quantity of voltage or current.
Put in a different manner an Analog signal is continuous in time and also continuous in value.
Uses of Analog 
Analog signals have a number of uses. AM and FM radio, for instance, are signals that are transmitted in analog. Telephones (at least simple, older telephones) use analog signals to transmit voice data to the phone central office. Many electrical components, such as sensors, will output analog data, because of the accuracy that can be obtained from analog signals.
Digital signals are different from analog signals in that there are generally only two levels of voltage: high and low. These different voltage levels are put into a sequence to describe the value being transmitted. For convenience, regardless of the actual voltage levels used, a "high" is called a 1, and a "low" is called a 0. Each signal level must be transmitted for at least a certain period of time called the Bit Time. A single signal level for a single bit time is called a Bit.
From bits, we have Binary Numbers, a collection of bits that can be arranged to form larger quantities than the simple numbers 0 and 1.
Uses of Digital 
Because bits can only be a 0 or a 1, digital transmissions don't have the same amount of accuracy as analog signals. Also, digital systems need to have complicated digital circuitry to read and understand the signals, that can cost more money then analog hardware does. However, the benefit is that digital signals can be manipulated, created, and read by computers and computer hardware.
One of the best examples of digital signals are the control signals and data that are in use on your computer. Computers are almost completely digital, except for the sound card (which produced analog sound signals), and maybe a few other peripherals. Cellphones now are mostly digital, and the internet is a digital network.