Muso: means 'Peerless' or 'without equal'.
Jikiden: means 'directly transmitted' ie from teacher to pupil.
Eishin: is the name of the seventh headmaster of the school.
Ryu: means 'School' in the sense of a style or tradition.
So, Muso Jikiden Eishin Ryu is "Eishin's peerless, directly transmitted school". It is a Koryu or 'Old School' with a long history.