I am a complete novice and trying to understand Bitcoin's functionality. I really don't understand how and why there is such a price appreciation since 2009 till now?
Bitcoin has a very small monetary supply; only 21 million BTC will ever be created. Because the supply is limited, increased demand -- from adoption, speculation about future adoption, etc. -- drives the price up.
I often hear where everyone talks about its security but then the details of the people are already with exchanges and exchanges are getting hacked at times and people are losing their digital currency so then how it is safe and anonymous.
There are different kinds of security. Bitcoin is "secured" by an incredible amount of computing power, to the point that most people consider its ledger immutable and its payments irreversible.
Exchanges are trusted third parties that hold custody of bitcoins on behalf of customers. When exchanges get hacked, that's a matter of their own faulty security practices. It has nothing to do with
Bitcoin's security.
In many posts and discussion threads, I have read where some say Government will stop the digital currency and some say Government will adopt it. What are the possible exact reasons for the same?
Some small governments have banned cryptocurrencies. Most are trying to regulate them, and some (like Japan and Malta) are embracing them. I think that over time, most governments will realize the need to embrace cryptocurrencies for the sake of their country's economic growth and fiscal wellbeing.
What is the store of value of Bitcoin apart from the medium of exchange?
Fiat currencies -- dollars, euros, etc. -- can be freely devalued by governments and central banks. This can't happen with Bitcoin because its supply is enforced by decentralized software protocol. Because of its predictable supply and scarcity, Bitcoin is better than most other currencies or commodities at being "money."