孤单 is a very common, everyday word used in informal and personal contexts.
Expressing personal feelings: It's frequently used to tell someone how you feel. For example, “我今天有点孤单” (Wǒ jīntiān yǒudiǎn gūdān) - “I feel a little lonely today.”
Showing empathy: You can use it to ask about someone else's well-being, especially if you know they live alone. “你一个人住,会觉得孤单吗?” (Nǐ yíge rén zhù, huì juéde gūdān ma?) - “Living by yourself, do you ever feel lonely?”
In media and art: The word is extremely common in song lyrics, poetry, and movie titles, often conveying a sense of melancholy, longing, or urban isolation.
Connotation: Its connotation is almost always negative or, at best, melancholic. It describes a lack—the lack of company. It is rarely used in a positive sense.