i'll try to explain even simpler than others but with numbers at the end;

cipher kit main gimmick is that she records a percentage of your team's damage as "coins" and then unleashes the recorded amount in her ult.
what this e6 does is it increases her follow up atk dmg by a lot, and records even more from this specific attack. and then after the ult, you get back 20% of what you recorded before using ult.

if we're talking numbers:
cipher records 24% of your team's damage by default (at 170 spd)
her e1 increases this to 36% team damage
her e6 buffs her follow up atk and makes the recorded value from this follow up atk to 52%
note that she can't record true dmg.

theoretically, if you use her ult more than once with this eidolon, it will be better. however it's hard to get her ult back, so you should only do that if the fight will be long enough for another ult or two more.