President Yoweri Museveni was a vocal supporter of and advocate the bill. He believes that social media encourages "gossip," according to BBC News. The law will go into effect as of July 1st, but it's not clear how the government will monitor its citizens or collect the tax.
This is certainly a strange way to regulate the use of social media within a country. It's possible there may also be a political angle here, as President Musaveni suspended access to social media apps and platforms in the run-up to the country's 2016 presidential elections.
Uganda isn't the only country looking to limit its population's usage of social media, though. Papua New Guinea recently announced that the country would block access to Facebook for a month to analyze how the population is using the service. It's not clear why the government needs to shut down access to Facebook in order to get this data, but clearly countries are interested in limiting citizens' use of social media.