In essence it means that the Bank of Uganda is free to implement its core policy responsibilities, which are monetary policy and bank regulation, without political interference. For example, the Government cannot give instructions to the Bank of Uganda with regard to setting the policy interest rate.
There is a very strong economic rationale for central bank independence, because independence gives monetary policy and bank regulation more credibility with the private sector, which in turn improves incentives for the private sector to act in ways which are consistent with low inflation and financial stability.