Being a fan of someone or something and idolizing them/it. Many people will define it as maniacal and obsessive but theres a separate definition for that. Its also a popular wordplay where you use it to show support to someone or something.
" i love bangtan sonyeondan, im a stan"
"Did you see yoongis latest mv daechwita??? We stan"
" we only stan feminists in this household"