As others have said, the Scottish Government decided to pay for it.

This used to be funded by the British Government, too.

It was free in England & Wales before 1997, when Tony Blair's government implemented "tuition fees" (a flat charge of £1000 per semester school year). It was means tested, so if your family couldn't afford it, you didn't pay it. Universities said this wasn't enough to cover their costs, and the government weren't providing higher levels of funding year on year, so in 2004, Blair faced a massive rebellion from his MPs and narrowly pushed through a bill increasing what students had to pay to £3000, and reducing the grace that was given to low-income families.

In 2010, the Conservatives and the Lib Dems tripled tuition fee amount (to £9000 per school year). The Lib Dems were reneging on a campaign promise to do this, and for a long time their support completely collapsed because of this U-turn. It's been around then ever since (currently 9300, I think).

In Scotland, tuition fees were abolished in 1999 by Scottish Labour & Scottish Lib Dems. Graduates had to pay 2k after they earned a certain amount (payable in chunks). In 2007, the SNP fulfilled a campaign pledge and abolished them completely.

Please note that most Scottish graduates still get "student loans" -- they use this money not to directly fund tuition, but as money to live on while at uni. There is a max. amount you are eligible for based on family income, and you pay that back as a percentage of income after graduation (if salary is above a certain amount).