The entire world is full of signals, both analog and digital data/signal are natural and artificial. Signals can be analog or digital. Figure illustrates an analog signal.
Analog Data / Signal
The term analog signal refers to signal that is continuous and takes continuous value. Most phenomenon in the world today are analog. There are an infinite amount of colours to paint an object (even if the difference is indiscernible to the eye), it is possible for us to hear different sounds and also smell different odours. The common theme among all of these analog signals is their infinite possibilities. 
Above Figure shows a typical representation of analog signal. Because the signal varies with time, time is plotted on horizontal (x-axis), and voltage on the vertical (y-axis). While this signals may be limited to a range of maximum and minimum values. There are still an infinite number of possible values within that range. For example the analog voltage that light the bulbs is clamped between -220V and +220V, but as you increase the resolution more and more, you discover an infinite number of values that the signal can be. For example, pure audio signals are analog. The signal that comes out of a microphone is full of analog frequencies and harmonics, which combine to beautiful music.
Digital Data / Signal
A digital signal is a physical signal that is a representation of a sequence of discrete values. The signal must have a finite set of possible values, the number of set which can be anywhere between two and very large number that is not infinity. Digital signal is one of two voltage value (0V or 5V) timing graphs of these signals look like square waves as shown in figure below. 