Someone indiscreet lacks discretion and doesn’t know when to keep things on the down low. Going to see your ex-girlfriend’s band with your new girlfriend would be indiscreet.
An indiscreet person would blab your secrets to everyone. An indiscreet person is loud, inappropriate, and thoughtless. While being discreet implies caution, being indiscreet is wild and careless. An indiscreet boss will correct your mistake in front of everyone, humiliating you. If you commit a crime and are indiscreet by running from a bank robbery with marked bills flying out of your pocket, you’re much more likely to get caught.