What does 厉害 mean, and in what context does it mean what?
It is somewhat similar in usage to the word great in English, with the following meanings I can recall:
Impressive or skilled:

他的功夫非常厉害。= He is very skilled in martial arts.
太厉害了，他是怎么做到的？ = Very impressive, how did he manage to achieve that?

formidable:

厉害的角色 = A formidable figure (not one to be messed around with)
厉害的手段 = formidable tactics (in a sporting game, or as part of political intrigue)

severe:

某某股跌得太厉害了 = Stock X has taken a severe fall (in value)

However, 厉害 is not usually the phrase/word of choice to describe a performance (of the arts).