The difference between analogue and digital data can be illustrated as the difference between a VHS tape and DVD --- both are methods for watching a film, but the VHS is an analogue method of playback and the DVD is digital.
Analogue data is a series of electrical pulses, frequently designed to represent what they embody. The example cited by PC Magazine is that of an analogue clock with rotating hands designed to imitate the way that the planet rotates --- giving time both a number and a visual representation. Radio waves are another example of analogue data.
Digital data is a numerical representation. All data on your computer is digital; digital data stores information in binary form, using ones and zeros to create the interfaces and data that you use on your computer.
The major difference between analogue and digital data is that digital allows for identical copies of the data; no matter how many copies you make of a photo file, the quality will not be lost. However, with analogue copies of a photo or tape, the quality is slightly degraded with each iteration.