What is the relationship between STARs, IAPs, and feeder routes?
Definitions
From the FAA's Pilot/Controller Glossary, an instrument approach procedure (IAP) is:

A series of predetermined maneuvers for the orderly transfer of an aircraft under instrument flight conditions from the beginning of the initial approach to a landing or to a point from which a landing may be made visually.

A feeder route is:

A route depicted on instrument approach procedure charts to designate routes for aircraft to proceed from the en route structure to the initial approach fix (IAF).

A standard terminal arrival (STAR) is:

A preplanned instrument flight rule (IFR) air traffic control arrival procedure published for pilot use in graphic and/or textual form. STARs provide transition from the en route structure to an outer fix or an instrument approach fix/arrival waypoint in the terminal area.

So you can see that a STAR and a feeder route serve the same general function: to allow IFR aircraft to transition from the en route structure (meaning Federal airways, the Victor, Tango, J- and Q-routes) to the beginning of an instrument approach procedure. The major difference is that STARs are published for busier airports to make things easier and more predictable from ATC's point of view; a STAR can contain any number of waypoints/fixes and, more importantly, can have altitude and speed restrictions pre-published at those fixes so ATC doesn't have to issue them to each individual arrival.
Example
Let's look at the ILS Runway 11 approach into Portland International Jetport (PWM). We can see that there are three Initial Approach Fixes: Kennebunk VOR/DME, BUXTO intersection, and PARSO intersection. If you can somehow navigate to any one of those three fixes, you can follow the approach procedure to safely get down to the ground (or at least pretty close to the ground).



Now say, for example, you're navigating via V93 from the southwest. When you reach CON you could continue to follow V93 to ENE and start the published approach by flying on the ENE030 radial to BUXTO and performing the hold-in-lieu-of-procedure-turn. But that takes you rather out of your way, so if you could you'd rather start the approach at PARSO and avoid having to perform a procedure turn.
Well, PARSO is on V3, so you could fly CON.V93.SATAN.V3.PARSO. But that still isn't the most direct route.
Happily for you there's a published feeder route starting from CON! When you arrive at the VOR/DME you leave the airways and navigate on the CON067 radial directly to PARSO. Hooray!


Enroute L-32 IFR chart

This plan might work if you were flying a Skyhawk at 5000 feet. But say you're flying Southwest 1982 from Baltimore, descending out of the flight levels at 250+ knots. ATC would rather have you flying a certain procedure that's the same as all the other jets coming in to Portland, and your dispatcher knows this—so they've filed for, and ATC has cleared you via, the SCOGS THREE arrival.



Some time before you reach SAACO, and probably long before then, ATC will tell you to expect Runway 11. Therefore, when you reach SAACO, you will make a left turn towards BIDDE and continue following the published route until you reach BUXTO. By this point ATC has cleared you for the ILS Runway 11 Approach, so you transition from the STAR directly onto the instrument approach. Note that you arrive at BUXTO on a track of 081, meaning you only need to make a 29º turn to intercept the localizer (track 110).
A different example
The SCOGS arrival is designed to get you from the enroute structure down to the ground with little-to-no ATC intervention. But at many even busier airports, the arrival will not smoothly transition onto an instrument approach. Instead, you will depart the final fix on a published heading (likely the radar downwind heading) and expect vectors to final from ATC. This allows ATC to give you extended vectors, or shortcuts, as necessary to account for the mixing of different arrival streams. The arrivals into Charlotte/Douglas International are like this, for example the CHSLY FOUR:



If you're landing Runway 23 the arrival has you navigate to JEPHS, the initial fix for the ILS approach for that runway. But if you're landing Runways 18 you come off the arrival on a heading for a left base, while if you're landing Runways 36 you're on a heading for a right downwind.