三顾茅庐

In the third century, China was divided into three kingdoms: Wei in the north, Shu in the southwest and Wu in the southeast. Shu was a weak state. The head of Shu, Liu Bei, was searching for talents everywhere for the kingdom. He heard of a very wise and knowledgeable man called Zhuge Liang who lived in Longzhong in Hubei province. So Liu decided to invite him to be his prime minister to help strengthen the State of Shu. 

In the year 207AD, Liu Bei with his sworn brothers（拜把兄弟） Guan Yu and Zhang Fei traveled to Longzhong to ask Zhuge Liang to assist him. But Zhuge was not at home. Thus they had to return disappointedly.

Later, they came again. But again they failed to see Zhuge, because he had been wandering about for days and hadn't yet come back. This time, Liu Bei left a note expressing his meaning.

Some days passed, Liu wanted to make a third visit. Guan and Zhang wanted to stop him, but in vain. This time, Zhuge Liang was at home but he was sleeping. Liu let Guan and Zhang stand at the door, and he stood by the bed. When Zhuge woke up and saw him, he was moved by his sincerity. He complied with Liu's request and became his prime minister. With the help of Zhuge, Liu enlarged his territory and his kingdom became as strong as the Wu and Shu.

Later, people use it to describe people who invite someone in all sincerity and eagerness.