How numbers convey information is an important aspect of our understanding of numbers(apart from the fact many practical applications that it has.) Besides there use in counting, algebra and other sciences they have their use in information processing. Information processing is one of the most widely used aspects of computing and our day to day interaction with computers is generally based on some sort of information processing.
Let us discuss this aspect of numbers. The first two numbers 0 and 1 tell us about the absence or presence of some object(or information). If some object is absent, we say that there are 0 instances of that object present. Take for example apple. Say , somebody has never seen an apple. In numbers terms he has seen zero apples. The said person can never visualize apple and he has absolutely no idea about apple.(Unless somebody has already told him/her about its properties.) .This implies the said person has no inormation regarding the apple. So zero means absence of information.
Now say we give the same person one apple. This one apple will convey all the information that the person is able to absorb about that one apple and give the general idea about the different varieties of apple. Now suppose we give him some more apples which are identical to the first one . Now even though he has more than one apple it will not increase awareness about the apple in any way. That means that single apple is sufficient to inform him.
So what do one and zero mean. Theoretically, at least, zero conveys no information whatsoever about an object, whereas one instance conveys all the information about that instance. I used the word theoretically because of practical limitations imposed by the presence of only one instance.
Now where does two fit in. Why did computer uses 2 as the base for all information processing ? To answer this let us first how do we convey information. Let us say we have two humans A and B. B decides to leave earth with a transmitter which transmits wave of different frequencies and A has a receiver which decodes the frequency that is transmitted. B lands on some new planet and finds that his transmitter can communicate only one frequency. A finds that he is receiving a constant signal from B. Even though they are communicating no effective communication or information exchange takes place as transmission has a single or one state. Now say suddenly B finds that he can tune his transmitter so that it can transmit at two frequencies instead of a single one. Now B can transmit at least some information to A (some information which has only 2 states or 2 values or at least limited to 2 values) .
This means that at least two states are required to transmit some information. This means at least 2 is required to convey state information. All these numbers (2 and numbers greater than 2) convey us different states of an object. In nature apple come in different shapes, sizes and tastes. To represent all these ‘states’ of apple we require numbers greater than 1. So numbers 2 and above represent ‘variety’.