Combining them literally gives you: “Without a home (that one is) able to return to.” This structure emphasizes the loss of a destination and a safe haven, making it a very powerful and descriptive term.
In Chinese culture, the 家 (jiā) is the bedrock of society and personal identity. It is the source of support, reputation, and continuity through generations. To be without a 家 is to be cut off from one's roots and social safety net. Therefore, 无家可归 is a statement of profound tragedy. It speaks to a failure of one of the most fundamental pillars of a person's life. A useful comparison is to the English word “homeless.” While “homeless” accurately describes a person's living situation, it can sometimes be used in a neutral, sociological, or even bureaucratic context (e.g., “homeless services,” “a homeless man”). 无家可归, on the other hand, is almost never neutral. It carries an inherent weight of sympathy, sadness, and the deep cultural pain associated with being adrift and without family. It evokes empathy immediately, focusing on the emotional state of having no place to *return* to.
This idiom is common in both formal and informal contexts.
The connotation is consistently negative and sympathetic. It is a serious term that conveys a difficult situation.