A TFSA is a tax free savings account. It is a type of account where you can buy various investments like stocks, bonds, or funds (mutual, exchange traded, and money market). There are some other options but it's best to see what your bank or broker will allow.
You probably specified the type of investment when you opened the account. You can look at your statements or maybe online to see what you're invested in. My guess is some kind of HISA (high interest savings account). This is kind of the default option for banks.
The government created these accounts for a variety of reasons. The main stated reason was to encourage people to save.
Obviously they also do things to get votes. There was an outcry after the change to a type of investment called "investment trusts". This could be seen as a consolation prize. These can be valuable to seniors for many reasons and they tend to vote more often. There was also an election promise to eliminate capital gains taxes in some fashion.
It's not profitable for the government, in fact it supposedly cost the federal government $410 million in 2013. Banks make money by investing your deposit or by charging fees.
You can see what every tax break 'costs' the government in lost revenue here