Carrier Imposed Surcharge is the "new" name for "Fuel Surcharge" (which usually gets the YR or YQ identifier in the fare construction).
Scrutiny of the "fuel surcharge" has increased substantially as oil prices have plummeted, but YQ failed to fall in parallel. Rather than continue the charade of this being a fuel related surcharge, it's just been renamed to a general catchall addon cost.
It survives because corporate discounts are often applied to the base fare, pre application of the surcharge (so a "50% corporate discount" can actually be substantially less in the context of the final payment made).
It also provides some protection against some of the incredibly complex and convoluted routes that have become possible as airlines have got into JVs. (The routings available between BRS and LAX cover all travel through just about every single US hub airport). By charging a per-sector "surcharge", there's less risk the airline will lose money on someone choosing a cheaper, more esoteric routing.
The most frustrating part of YQ for me is the huge cash cost it dumps on frequent flier mile redemptions. In the case of LH, and their increasingly perverse application of YQ, sometimes using miles and paying their "standard YQ" is substantially higher than just buying a cash ticket (with "discounted YQ") outright.
APD is charged by each country on your itinerary to which it applies. UK APD is calculated on the distance to your final ticketed destination. IE APD is a fixed cost. It's possible to end up paying multiple APD fees to multiple countries on a single itin. I know of an increasing number of BRS fliers who hop over to DUB on the EI flight (APD cost £13) and then turn right around on BA to LHR and onto longhaul, because it can save a big amount on both APD *and* airfare.
/end rant.