In a parliamentary system, the leader of the government is not elected by the voters. Instead, voters elect members of parliament. Then the members of parliament choose one of their members as the leader. The leader is often called a “prime minister”.
Normally, if a majority (more than half) of the members of parliament are from one political party , that political party can select the leader. If not, several political parties might need to join together in a “coalition” to create a majority. They can then choose the prime minister.

(Source: UK government, via Wikimedia Commons.)
In a parliamentary system, the prime minister is the head of the government. This is usually the most powerful position in the country. Parliamentary countries usually have a different “head of state” , such as a king or queen or president. The head of state often does not have as much power as the head of government.