"engagement" means two elements coming together and interacting. It usually refers to marriages but it can be used for all kinds of things. Two armies fighting each other is a "military engagement". "Brand engagement" is a marketing term which refers to how customers interact with a brand. For example, the way people emotionally or rationally develop feelings towards McDonald's or Facebook. This connection between the brand and the person is known as the Brand Engagement. "Brand engagement gone wrong" means the feelings and opinions towards a brand have started to become negative. Again, Facebook could be an example of this. There is a lot of negative news about that brand nowadays.

I can tell you it's not about our traditional use of the word engaged, meaning betrothed. In recent years, engagement has come to mean something similar to involvement or interest.

You need to provide more context, Farid. The partial sentence isn't enough. Can you post a few preceding sentences ?