If you go around explaining to an average person over 40 what it means to be casually "seeing" someone, you might see their eyes dart open with the implicit implication that you are downright promiscuous. Three dates in without labeling your partner as "boyfriend/girlfriend" is considered, by many, to be kind of odd. Five dates later? They should have already met the parents and set the wedding date.
The Chinese phrase for "date" is 约会 (yuēhuì), with the character 约 having a less than casual original meaning. As a matter of fact, it's exactly the opposite of casual. Like many other characters, 约 is connected to "silk", or 丝, which you can see from the "silk" radical, 纟, on the left. In seal script, the silk radical appears as a bundle of tied silk treads. So, the original meaning for 约 is "to bind, to tie up". Its right radical, 勺, was supposed to represent the character's pronunciation, but the sound changed over time.
Later, 约 developed more abstract meanings along these lines. 约束 (yuēshù) means "to keep within bounds; 制约 (zhìyuē) means "to check, to restrict" as in 制约平衡 (zhìyuē pínghéng) or "checks and balances"; and 约 could also mean "limit" as in 节约 (jiéyuē), or "to economize, to save". For instance, a common sign in an environmental campaign is 节约用水 (jiéyuē yòngshuǐ), or "save water".
With 约, things often have a binding effect, from more serious international affairs such as international conventions (国际公约 guójì gōngyuē), treaties (条约 tiáoyuē), and legal contracts (合约héyuē)—to personal, quasireligious contracts like an engagement, or marriage contract as in 婚约 (hūnyuē). To honor an agreement is to 履约 (lǚyuē). To break one's promise and violate the contract is 违约 (wěiyuē).