Triggered is a synonym for 'angry'. The word was born from the psychiatric industry which warns people with PTSD of words or images called 'triggers' that could cause flashbacks. To prevent people from having flashbacks, it is considered polite in mental health circles to notify people with PTSD beforehand if something might contain something that could cause flashbacks or association with past trauma. This coping mechanism for PTSD sufferers was then used by femoids on Tumblr to warn of any possible thing that could cause any negative emotion, including but not limited to feeling bad about hearing the behaviors of modern Western women in any negative light, however true that light was.
Because of how ridiculously wide this coping mechanism for PTSD was deployed to make anything that offended mentally ill women automatically 'abuse or trauma'... the manosphere began taking it as an honor to offend the easily offendable.. Especially if it meant pointing out something true and important that was being hidden solely under the defense of it being hurtful to women's feeling.
Thus a culture (mostly 2016 4chan culture) was created dedicated to 'triggering' people who used feelings as a defense for being dishonest or hiding true information.
Studies have demonstrated that being triggered, moderate trauma and adversity are beneficial for psychological functioning, see antifragility.