In the Bitcoin network, user transactions are grouped in blocks and recorded to a digital public ledger called a blockchain. Miners are in charge of this task, and receive a mining reward in the form of bitcoins for each block recorded.
The amount of bitcoins rewarded for each block decreases with time: it is halved every 4 years. This event, the moment when the mining reward is divided by 2, is commonly called “Bitcoin halving”. Other denominations are used: “reward drop”, “reward halving”, or simply “the halving” or “the Halvening” which is a popular meme among bitcoiners.
When Bitcoin was created in 2009, the initial reward was 50 bitcoins. In november 2012, it dropped to 25btc after the first halving. The second halving will take place in July 2016, decreasing the reward to 12.5btc.
As any freely traded asset, Bitcoin price depends solely on demand and supply. The evolution of bitcoins supply is hard coded and is known to everyone, so it all depends on the evolution of demand. Bitcoin being a very young currency with much room to grow in use and value, I would personally bet on a price increase. How much? When? It remains 100% unpredictable. One thing is certain though: at the time of Halving, the supply reduction will already be priced in the exchange rate, thanks to market anticipation. So don’t expect a big price movement on Halving Day.
Note that other examples of halvings are available for comparison. The first Bitcoin halving occurred on the 28th of November 2012. On that day the price went up +1.7%, a negligible move. However the preceding and following months showed continued growth and led to the famous early-2013 rally (from 13$ to 260$ in 4 months). More recently, the Litecoin, a Bitcoin clone, passed its first halving on August 25th, 2015. Two months before, a wild speculative rally took the price from 2$ to more than 8$, before crashing back to 3$.
What is certain for this second Bitcoin halving is that similar wild, speculative, short-term rallies and crashes will occur. The interesting observation will be, on a larger time-scale, to see if the up-trend that Bitcoin price has been experiencing since its inception in 2009 will continue its path.