A big servant is bigger than the rest of the servants. One type of servant is one who serves the people (as is the case with this one). A big servant is someone high up in the realm of serving the people. So, let's call this big servant a minister or cabinet member. Big cheese.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
She was fired because she forgot to hand out the documents to the cabinet members before the meeting.