"explicit" in adjective form can mean "stated clearly and in detail, leaving no room for confusion or doubt" or "describing or representing sexual activity in a graphic fashion".
The latter definition can be expanded to mean things inappropriate for a general audience, such as "I don't want my kids listening to explicit rap albums" (In fact, when a CD case is labeled "Explicit", it means it contains sexual references and foul language)
"my personal life" is generally things you want kept secret from others unless you chose to share it with someone, typically those are close friends, mates, etc.
Without any other context, this sentence seems to be implying that "She" is an antagonist, maybe an ex-girlfriend or spouse, is revealing some rather personal details in an inappropriate forum.