Leibniz was a German polymath and philosopher who occupies a prominent place in the history of mathematics and philosophy, having developed differential and integral calculus independently of Isaac Newton. Leibniz held that atoms were panpsychic and modified Bruno's theory of monads. Leibntiz meant his model to be a superior alternative to the theory of atoms that was becoming popular in natural philosophy at the time. Leibniz was a rationalist and believed one could arrive at truth just by thinking things through.
When Leibniz died in 1716 there were several people talking about atomic theory but it was over 80 years before Dalton produced the first empirical model of atoms and it has gone through many changes since then and today it is impossible to produce a satisfactory philosophical interpretation of quantum physics and although the standard interpretation (Cophanagon interpretation) is materialistic there are other competing idealistic interpretations that are very similar to Leibniz's monad theory.
Monads were an atomic theory in which the world is made up of an infinity of simple substances called ‘monads’. As defined in the Monadology §1, ‘The monad … is nothing but a simple substance, which enters into composites’ (T19. 1). These simple substances are the basic constituents of reality, and it is a requirement that they are immaterial or non-physical.
Like the early atomic theory, simple substances are capable of being neither created nor destroyed nor divided. They were understood to be substances that combined to create bigger objects and there are composites, which are collections or aggregates of simples, the features of which are explicable by features of the simples of which they are made up. Yet because these simple substances do not themselves consist of any parts, Leibniz describes them as the ‘true atoms of nature; in a word, the elements of things.’
However, there are also several ways in which Leibniz's monads were different from atoms. According to atomic theory, atoms are made of inert matter whereas monads have mental properties and each monad has a unique perspective on the universe but also contains within itself all the past and future events of the universe.
Furthermore, all monads reflect the whole world, each with their own unique different perspective. So each monad reflects the whole system, but with its own perspective emphasised. If a monad is at place p at time t, it will contain all the features of the universe at all times, but with those relating to its own time and place most vividly, and others fading out roughly in accordance with temporal and spatial distance. Because there is a continuum of perspectives on reality, there is an infinite number of these substances. Nevertheless, there is an internal change in the monads, because the respect in which its content is vivid varies with time and with action. Indeed, the passage of time just is the change in which of the monad's contents are most vivid.
All of the aspects of monadology mentioned above are a useful way of understanding the real world as science and religion understand it, but there was one more aspect that Leibniz included in order to preserve the western God, which is not necessary and that is “pre-established harmony”. Pre-established harmony (harmonie préétablie) claims that every "substance" only affects itself, but all the substances (both bodies and minds) in the world nevertheless seem to causally interact with each other because they have been programmed by God in advance to "harmonize" with each other.