Analog vs. Digital Signals
Signals found in nature are analog. Analog signals are continuous in time and amplitude; when plotted they form a continuous curve and can closely represent natural phenomena.
Digital signals are discrete in both time and amplitude. They involve sampling, so values change only at sampling points. They also involve quantization; in digital circuits signals typically take only the values 0 and 1.

Circuit Classification
In simple terms, circuits that process analog signals are analog circuits; circuits that process digital signals are digital circuits.
Circuits that handle both analog and digital signals, such as digital-to-analog converters and numerically controlled oscillators, are called mixed-signal circuits. When forced into a binary classification they are generally considered analog.
The components used are not the defining factor. MOSFETs, BJTs, and even vacuum tubes can be used to implement either digital or analog circuits. Integrated circuits commonly combine analog and digital circuits on the same chip, using essentially the same basic devices.
Practical Distribution
Most common circuits are digital, because large-scale digital circuit design is far easier than large-scale analog design; analog computers were therefore abandoned early. Today, analog circuits are generally concentrated at input/output and power module stages, for example in wireless and wired transceivers, clock generation circuits, and bandgap reference sources. Computational functions are now almost entirely implemented by digital circuits.