Often used in formal or written contexts, especially in compounds like 利便性 (convenience, ease of use). As a standalone noun/adjectival noun, it is less common than 便利.
The city improved the roads to increase the convenience of the area around the station.
The convenience of transportation in this area is improving year by year.
利便性を重視して、駅近の物件を選んだ。
Prioritizing convenience, I chose a property near the station.
This facility exists for the convenience of the residents.
不便 means 'inconvenient', the direct opposite of the convenience expressed by 利便.
Compound of 利 (benefit, advantage) and 便 (convenience, facility). The exact historical derivation is uncertain, but the combination naturally conveys the idea of convenience.