Whenever you break a subroutine on a piece of ice, you may pay 1 cred to break 1 additional subroutine on that ice.
When would I need this card? With most icebreakers, it's 1 cred to break a subroutine.
As of right now, there are two situations in which E3 feedback implants are useful.
The first is that it isn't always 1 cred to break a subroutine. Aurora, Peacock, Battering Ram, and Wyrm all cost more than 1 cred to break a subroutine. Two of these (Aurora & Peacock) are the same faction as E3 feedback implants. So it's feasible that you'd save a little bit of money over time.
The second use is against bioroid ice. Bioroid ice subroutines can be broken by spending a click. So with E3 feedback implants any bioroid ice can be bypassed by paying 1 click + 1 cred/remaining subroutine. Which makes things like Janus only cost 1 click + 3 creds.
If there are things added in the future that allow breaking subroutines via non-icebreaker methods, E3 implants would also be useful in those situations.
EDIT: There was discussion about whether or not E3 feedback implants could be used as the triggering condition for itself, so here's a link to a thread on BoardGameGeek where this got answered. (It does trigger itself) http://boardgamegeek.com/thread/910289/e3-feedback-implant-official-answer
As more cards come out, new synergies will obviously appear, but I think its best use at the moment is against some of the incredibly tough Haas-Bioroid ice which allow the runner to spend clicks to break subroutines.
For instance, Janus 1.0 is an 8 strength HB ice and has four subroutines which read Do 1 brain damage
, but allows the runner to spend clicks to break subroutines, one click breaks one subroutine. It might be very expensive in credits to beef up your icebreaker of choice and break all four subroutines, or expensive in clicks (if you even have enough) but with an E3 Feedback Implants, you could spend one click and three credits to break all the subroutines, which is much cheaper.
The rulings on e3 Feedback Implants from the Official FAQ:
e3 Feedback Implants triggers itself, so the Runner can break all subroutines on a bioroid ice by paying credits after spending a single click.
Here are some situations where e3 Feedback Implants can really be useful.