Human life, length, breadth, time, mass, area, measurements, signals, noise, light , energy - these are all continuous. Every thing we feel, see , think, do is a continuous quantity or analog in nature.
But the analog signals are mixed with noise and are difficult to separate from noise. Noise is present everywhere. Degradation of components due to age or other problems is difficult to deal with analog systems. But analog systems are simple, consume less power. But their range of good quality performance is not large.
Need for digital comes in, when information is stored, or transmitted, as we face difficulties when we retrieve or receive information signal.
With digital systems, we transmit information, in terms of a signal, which is analog only, but we code it as zero and one. On receiving end, we check the signal level and decide if it is 0 or 1. If the noise level is not much compared to signal, then we can completely recover the signal and regenerate the signal exactly and 100% correct. This is not possible wit h analog systems.
For doing this extra work, the digital systems consume more energy. But digital systems can be made more modular and flexible. With digital systems, one can dynamically program the circuit. This cannot be achieved so easily with analog systems. Quality is improved drastically with digital systems. After a long time, the data stored in analog systems may be lost or degraded, but digital systems will retain correctly.
Digital systems donot change the nature of world. They only process digitally. The analog signals are regenerated up to a high quality analog signal as close to reality as possible, in a CONTROLLED fashion.