Great song! 'Ain't no sunshine when she's gone' is a shortened form of 'There ain't no sunshine when she's gone' . In standard English, this means 'There is no sunshine when she's gone' . As you've learnt, 'ain't' is a non-standard, colloquial form for the negative of 'to be' and 'to have'. Another non-standard feature of sentences with 'ain't' is double negation. For example 'I ain't got no money' means 'I don't have any money'. 'Ain't' is nearly always followed by a second negative. And why do we use 'ain't' so much in songs? Because it often sounds better!

Ain't is slang, not good, grammatical English. The song says "Ain't no sunshine when she's gone" meaning that when the girl is not there, he feels like the sun is not shining, meaning he is sad or depressed. In proper English, you should not put two negatives together (Ain't and no), but it is done in informal or colloquial English. The songwriter should have said "There isn't any sunshine when she is gone", but it just doesn't have the same rhythm, does it?

Ain't no sunshine means there is no sunshine. There is no sunshine when she's gone. It's like saying there isn't any sunshine. It isn't standard English, yet is used informally. Other examples include I ain’t got no money. = I haven't got any money. Ain’t no man like him. = There is no man like him. All these examples are dialectal. Double negatives are grammaticallly incorrect in standard English.