Usually it means someone who is really good at something. Sometimes (and this is NOT infrequent) it has a negative connotation.
For example, 那個女人很厲害。This could mean that that woman is very good at something, like cooking or painting, or singing, etc. However, it often also means that "that woman is very manipulative," and that you have to be careful and watch out so that you do not fall victim to her feminine wiles.
As a note about the sexist nature of many languages, if you say that a man is 厲害,the negative connotation is not as strong.
It like saying saying, in French, "un grand homme" (meaning a great man), but a "une grande femme" sounds more like a woman tall in height.