When you put them together, 眯 (to close your eyes) + 一会儿 (for a little while) literally means “to close your eyes for a little while,” perfectly capturing the idea of a short, refreshing nap.
In many Western cultures, napping during the workday is often seen as lazy or unprofessional. In China, however, taking a short nap after lunch is a widely accepted and even encouraged practice, known as 午觉 (wǔjiào), or the “midday sleep.” “眯一会儿” is the action you take to have a `午觉`. It's common to see office workers resting their heads on their desks for 20-30 minutes after eating, or students napping in the library or classroom. This isn't viewed as slacking off. Instead, it's rooted in a cultural belief, partly influenced by principles of Traditional Chinese Medicine (TCM), that a midday rest is essential for maintaining health, balance, and productivity for the rest of the afternoon. While the West has the concept of a “power nap,” it's often framed as a productivity hack or a bio-hack. In China, the post-lunch nap is simply a normal, expected part of the daily rhythm, much like the lunch break itself. “眯一会儿” is the casual, everyday term that brings this cultural practice to life in conversation.
“眯一会儿” is a highly frequent, informal phrase used in everyday conversation. It's almost never used in formal or written contexts.