While a simple phrase, 开灯 and its opposite, 关灯 (guān dēng, turn off the light), are tied to the important Chinese cultural value of 节约 (jiéyuē) - frugality and conservation. In modern China, you will constantly encounter reminders to save electricity. The phrase 随手关灯 (suíshǒu guān dēng), meaning “turn off the lights as you leave,” is posted in nearly every school, office, dormitory, and public restroom. This isn't just about saving money on the electricity bill; it's seen as a social virtue, a sign of a responsible and considerate person who doesn't waste resources. Compared to Western culture, where leaving a light on might be seen as a minor oversight, in China, it's often viewed as a small but meaningful reflection of one's character. Being reminded to 关灯 is a common and normal part of daily life, reflecting a collective consciousness about resource conservation.
开灯 is a high-frequency, neutral term used in all levels of formality.