Meaning:
This is the acronym of the English term “background music,” which refers to a piece of music intended as an unobtrusive accompaniment to an activity or to provide atmosphere in a film, TV show or video game. As background music often accompanies the entrance of an important character in a film or game and leaves an impression on the audience or gamer, Chinese netizens use the saying “自带BGM” (accompanied by one’s unique background music) to describe someone who is very special.
Example:
A: 听说你表妹喜欢同校的一个男生？
Tīngshuō nǐ biǎomèi xǐhuan tóngxiào de yīge nánshēng？
I’ve heard that your cousin has a crush on a boy in her school.
B: 是的，这个男生又高又帅，爱打篮球，属于偶像剧里自带BGM的那一类人。
Shì de，zhège nánshēng yòugāo yòushuài，ài dǎ lánqiú，shǔyú ǒuxiàngjù lǐ zìdài BGM de nà yīlèirén。
Yeah. The boy is tall and good-looking and likes to play basketball. He is the kind that you often see in a romance drama who makes an entrance accompanied by background music.