Two readings: 便 (convenient / then / informal) covers the overwhelming majority of compounds - 方便, 顺便, 随便, 便利. 便 appears almost only in 便宜 (cheap) and the obese-sense 便便.
grammar
As an adverb, 便 is the literary cousin of 就 - same meaning (then / right away / in that case), more formal register. Common in written Chinese and set phrases like 即便 (even if) and 以便 (so that).
Left person radical - the side-form of 人, a standing figure. The indexing radical (Kangxi #9). 便 is about people making things easier for themselves, so the human focus is literal. Same radical heads 你, 他, 们, 住 - the bulk of person-related vocab.
Right component 更 - historically supplies the sound (gēng → biàn, with heavy Old Chinese drift). It also carries a faint semantic echo: changing things to suit a person = adapting for convenience. The 便/便 split inside this character reflects two old branches of the same word.
