过 (guò): The core meaning is “to pass,” “to cross,” or “to go through.” In this context, it signifies the passage of time.
日 (rì): This character means “day” or “sun.”
子 (zi): A very common noun suffix in Mandarin. It doesn't add much meaning here but makes the word “日子” (rìzi - days) sound more natural and colloquial.
Putting them together, “过日子” literally translates to “to pass the days.” This simple, literal meaning beautifully captures the essence of the term: living life one day at a time.
“过日子” is an extremely common, informal term used in everyday conversation.
Describing Married/Domestic Life: This is one of its most common uses. It describes the process of a couple managing their life together.
e.g., “They're a couple who really knows how to live life.” (他们俩真会过日子。) This implies they are frugal, practical, and work well together.
Describing Financial Hardship or “Getting By”: It can be used to describe the struggle to make ends meet.
General Description of Daily Existence: It can be used more neutrally to just mean “living” or “going about one's days.”
The connotation can be positive (praising someone's frugality and skill at managing a home), neutral (simply stating the fact of living), or negative (implying a hard or dreary existence).