请客 means to treat someone to a meal. In Chinese culture, fighting over who pays the bill is a common social ritual — offering to 请客 shows generosity and friendship.
Left speech radical — the indexing component, the contracted form of 言. Marks 请 as a polite speech act: requesting, inviting, treating someone. The radical is the first hint that the verb involves spoken courtesy. Same family as 说, 让, 谁, 谢, 课, 谈.
Right 青 supplies the sound exactly: qīng to qǐng with only a tone shift. The same phonetic family is highly regular (情, 清, 晴) — see 青 anywhere on the right and expect a qing-something reading. Faintly adds "pure" flavor fitting polite request.
