A government is a group of people who run a country. Like UK, the prime minister of Singapore is in charge of running Singapore. In other countries such as USA, it is run by a president. But both the prime minister and the president work closely with the government to come up with policies.
It is better to have a group of people running a country because there will be more discussion and better decisions will be made as compared to a single person working alone. It’s the same for science!
The government in the UK are elected by people to represent them when making decisions about the country – decisions like how much money should be spent on schools, or science or hospitals. We’ve got a Prime Minister to be the head of them, the MPs. A president is a bit like a prime minister, but even in the USA he has lots of people (senators and representatives) who are elected to represent the people. The president is the head of state in the USA, in the UK the Queen is the head of state. In both cases there is still a government, so they are quite similar.