Firstly, he presented the favourite mantra of modern people "everything happens by chance". Obviously, it is an important issue also to Theology as it denies the existence of God. Democritus has been called the first materialistic atheist in western history. Nevertheless, he was a happy and balanced man to the point that he was called by others the laughing Philosopher.
Democritus presented the idea in his amazing nature philosophy that everything is made up of invisible particles, atoms, that cannot be further divided. These are constantly moving and colliding in totally random manner in the empty space (keenos) and their collisions create different kinds of groups that give all matter its attributes such as colour, hardness, taste or weight.
When Albert Einstein said in the 1920'ies that God does not play dice he was essentially protesting against the developing notion that that everything in nature is essentially randomized on the particle level and that quantum mechanics with Heisenberg's uncertainty principle has destroyed all causality and determinism at the deepest foundations of physical existence.
Secondly, Democritus is very important for the simple reason that he was thinking it all.
This philosopher is a truly classic example of the power of human mind and its fabulous ability to figure out things visible and invisible, invent, innovate, create and destroy, love and hate. It is obvious to all of us today that Democritus did not have any empirical instruments to study atoms. He was just thinking about them.
It is first and foremost human thinking that has revolutionized Physics in our times. Of course, Einstein had empirical evidence from the many experiments in electromagnetism by many 19th century scientists. But his theories of special and general relativity were nevertheless thinking trips he made in his mind. Throw in some mathematics. Some of his thoughts were empirically tested during his life time and others have been tested only later when the necessary technology has became available. Like Democritus, Einstein was essentially thinking how things are. When the theory was beautiful that was it. Experiments for and against his ideas came only later.
Epicurus (341 - 270 B.C.) took very seriously what Democritus was teaching about the pure chance at the foundations of all that exists. If everything is just random movement of material particles so nothing really matters. Nothing has any real purpose and life and death are just plain game of dice. So what should we do? Let us be happy! Let us eat and drink for we shall die tomorrow.
This philosopher established a Garden school in Athens that became quite famous and people from near and far came there. Since everything is just colliding atoms there is no need for social hierarchies. Women and slaves were as much humans as the free men of Athens and were allowed to join in. The ethics in the Garden school may have resembled modern day ethics in the big cities. For if nothing matters but happiness let us really be happy as Richard Dawkin and friends are telling us.
I believe that unconsciously a number of modern men and women have adopted similar ideas as Epicurus was teaching in ancient Greece. Since we are just a random product of natural selection in the tree of life nothing really means anything. Let us be happy, let us try to make the best of this short life given to us before our atoms mingle with the atoms of the universe and perhaps become future building stones in a bee or a crocodile or a tree or some other human being. Round, round, round they go, those atoms and life forms fighting for survival after some lucky mutation caused by random radiation from the space.
By the way, apostle Paul agreed in principle with the logic of Epicurus:
If after the manner of men I have fought with beasts at Ephesus, what advantageth it me, if the dead rise not? let us eat and drink; for to morrow we die.
1 Corinthians 15:32 KJVA
He argues that if Christ has not risen from the death why bother martyrdom?
The same question of resurrection had also earned him many hearty laughs in Athens
Then certain philosophers of the Epicureans, and of the Stoicks, encountered him. And some said, What will this babbler say? other some, He seemeth to be a setter forth of strange gods: because he preached unto them Jesus, and the resurrection.
Act 17:18 KJVA
Now, we have to realize the great intellectual power of Democritus and Epicurus, the strength of their amazing brains, the deep logic and the imagination that established the existence of atoms over two thousand years ago just in the mind.
Yet, both these philosophers were wrong.
Modern nuclear physics have demonstrated that there is nothing randomly about the atoms. They are masterpieces of harmonic order and design so admired by ancient Greeks. We only need to study the atomic tables of basic matter to realize this and the deeper we get into the atoms the more amazing is the order we see there.
And since atoms and molecules are not random at all the application of this chance principle to life by Epicurus was also built upon faulty foundations.
So is the life of many modern man and woman who still erroneously think that evolution is guided by random mutations and environmental factors and fail to realize the wonderful order that exists in the location of each and every amino acid in those marvellous DNA molecules.
Or perhaps they refuse to realize it because accepting the fact that God has created man and woman brings with it serious consequences. The fallacy of a dice throwing God or blind faith in atheistic materialism are convenient for us exactly because they let people to imagine that they have turned into something like God by themselves - the familiar song of the Devil from the Garden of Eden, the spirit of Prometheus.