Simplified Chinese character 约

It means arrange, agree, or about, depending on its neighbors.

约会 can mean a meeting or date; 约定 is an agreement; 约束 means restraint; 大约 marks approximation; 节约 means to economize. Read the whole word: 约 has related senses, not one fixed English equivalent.

Where does 约 come from?

It comes from an older character associated with binding.

An ancestor of 約 appears in writing from the ancient Chinese state of Chu during the Warring States period, on slips and silk. This is an early attestation, not a confirmed first appearance of today's simplified form 约.

The Han-era dictionary Shuowen Jiezi explains 約 through wrapping and binding. In its character analysis, 糸 (thread) supplies the meaning and 勺 the sound; 纟 is the simplified counterpart of 糸. The binding idea connects with agreements and restraint, but does not date each later meaning.

Does 約 mean the same thing in Japanese?

No; the shared characters can mean different things by language.

Japanese 約束 means a promise or appointment, while Mandarin 约束 normally means restraint or restriction. The Korean word 약속 is historically connected to the same characters 約束 and means a promise or appointment. The familiar-looking compound does not guarantee the same meaning across languages.