The most basic reason that affects the price of Bitcoin is supply and demand.
Supply:
The total supply of bitcoins is affected in two different ways.
First, the Bitcoin protocol creates new coins at a fixed rate. When miners process blocks of transactions, new bitcoins are rewarded to whichever miner solved the block. By design, the rate at which new coins are rewarded is purposefully halved over time (approximately every 4 years). This can create a scenario in which the demand for bitcoins increases at a faster rate than the supply increases, which can drive the price up.
The second way that supply is affected is by the total number of bitcoins that will ever exist, this number is capped at 21 million. Meaning once this many coins have been "minted," mining new blocks will no longer create new bitcoins. It is speculated that mining will continue to be supported by the existence of transaction fees.
Demand:
Essentially, the demand for Bitcoin is whatever someone is willing to pay for it. As bitcoin finds more and more use cases beyond pure speculation (transacting, merchant payment processing, store of value, etc.) the demand for bitcoin may increase. The relevance of other cryptocurrencies, changes in legal and regulatory policy, availability on exchanges and more may also affect the demand for Bitcoin.