Number of Bitcoins
Any currency derives its value in large part through rarity. Bitcoin is no exception, digital scarcity is created through a strict limitation on the addition of new currency units into the system at large, up to a limit of twenty one million coins. To promote the diversity of Bitcoin ownership and to bootstrap the mining security mechanism, coins are distributed in a time stretched fashion: full divestment of the total supply will not occur until the year 2140.
In all currency systems, there are actually two numbers that represent the scarcity of the token: the monetary base and the monetary supply. The base refers to the number of tokens that are considered to really exist, if they all were to be traded or individually owned. The supply refers to the number of tokens that people believe exist, through the abstraction mechanisms of pooled funding like banks, where multiple people simultaneously believe and act as if they own the same tokens.
The process through which the Bitcoin monetary base expands over time through the miner subsidy is quite simple. About every ten minutes a block is found which contains a coin subsidy, starting with the genesis block that contains a subsidy value of fifty coins. Block timing is governed by a self correcting algorithm that readjusts every two weeks, actually specified by every two thousand and sixteen blocks. The subsidy value reduces exponentially over time, cutting in half every two hundred and ten thousand blocks, meaning every four years. The subsidy values have little real importance, Satoshi Nakamoto designed the system to approximate the rate at which gold mines are developed.
Inflation and Deflation
Changes in a currency's monetary supply are called "deflation" and "inflation", for decreases and increases respectively, given equal demand. In many currency systems, the monetary supply is managed by an institution known as a central bank. Most governments and central banks attempt to prevent deflation and limit inflation through tools such as printing money, adjusting their lending rate, and altering the reserve requirements of the banks that they regulate.
Bitcoin works very differently: there is no central control, the supply of tokens that makes up the Bitcoin monetary base is based on a common convention that is cryptographically guaranteed between cooperating peers. Bitcoin is also much more practical to own in a way where no bank-like fractional reserve mechanisms are possible, meaning that the monetary base and supply figures are given to being much more closely related.
It's quite common to hear Bitcoin described as both a deflationary and an inflationary system, especially by people who view these as loaded terms. These descriptions are both correct and incorrect.
Bitcoin can be thought of as a deflationary system for two reasons. The first is that it is possible to lose Bitcoin forever, meaning that in the long term, all things being equal, the monetary base of Bitcoin will decrease and the value of all tokens will increase. The second is that the total wealth of the world is increasing: more things chasing the same number of Bitcoin tokens means more things exchanged per token.
Bitcoin can also be thought of as an inflationary system for two reasons. The first is that the supply of Bitcoin is on a delayed distribution cycle where coins are given to miners over a hundred years, meaning inflation of the monetary base over that period. The second reason is that fractional reserve operations are still possible using Bitcoin, and they may be used to an increasing degree over time.