Things that are consequential are important — extremely important. Electing a new president and having a baby are consequential. Killing a fly? Not so much.
It might help you remember the meaning of consequential to think of consequences — the results of something. Consequential events have consequences, because they are hugely important events. A little bit of rain isn't consequential, but a hurricane is very consequential. Slipping on the sidewalk is not usually consequential, but if you slip and end up in the hospital, that is definitely consequential. It's occasionally hard to tell whether something is consequential, at least until some time has passed.