Each of us faces discreteness daily. This is one of the properties inherent in matter. In the literal translation from Latin, the word discretus means discontinuity. For example, a discrete signal is a way of transmitting information when the carrier medium changes in time, taking any of the existing list of acceptable values.
Of course, the term "discreteness" is used in a broader sense. In particular, now progress in microelectronics is aimed at creating and developing SOC technology - “System on a Chip”. It is assumed that all the components making up the device are closely integrated with each other on a single substrate. The opposite of this approach is discrete schemes, when the elements themselves are complete products, connected by communication lines.
Perhaps now it is impossible to find a person who would not use a mobile phone or Skype on a computer. One of their tasks is to transmit a sound stream (in particular, voice). But since such a sound is a continuous wave, for its direct transmission would require a channel with high bandwidth. To solve this issue, it was proposed to use a discrete signal. It does not form a wave, but its digital representation (remember, we are talking about mobile phones and computers). From a wave, at certain intervals, data values are sampled. That is, a discrete signal is created. Its advantage is obvious: a smaller total data stream and the possibility of organizing packet transmission. The target receiver integrates all the samples into a single unit, generating the original wave. The larger the intervals between the samples, the higher the probability of distortion of the original wave. Discretization is widely used in computing.
Speaking of what a discrete signal is, one cannot but take advantage of the remarkable analogy with an ordinary printed book. A person reading it receives a continuous flow of information. At the same time, the data contained in it is “encoded” in the form of certain sequences of letters - words - sentences. It turns out that the author forms an original discrete signal from indivisible thought, as it expresses it by breaking it into blocks, using one or another encoding method (alphabet, language). The reader in this example gets the opportunity to perceive the idea of the author only after mentally combining the words into a stream of information.
Surely you are reading this article from a computer screen. But even a monitor screen can serve as an example where discreteness and continuity are manifested. Recall the old models based on CRT. In them, the image was formed by a sequence of frames that needed to be "drawn" several tens of times per second. Obviously, this device uses a discrete way to build pictures.
A discrete signal is the exact opposite of a continuous signal. The latter is a function of intensity versus time (if you imagine it on the Cartesian plane). As already indicated, one example is a sound wave. It is characterized by frequency and amplitude, but naturally does not interrupt anywhere. Most natural processes are described in this way. Despite the fact that, nevertheless, there are several ways to process a continuous (or analog) signal that can reduce the data flow, it is discrete that is common in modern digital systems. Partly due to the fact that it can be quite simply converted to the original, regardless of the configuration of the latter. By the way, it is worth noting that the terms “discrete” and “digital” are almost the same.