What is the role of an intermediate fix?
The Pilot/Controller Glossary can shed some light on your question.

The GPS approach is the clearest example of an Intermediate Approach Fix. 


  IF/IAWP− Intermediate Fix/Initial Approach Way- point. The waypoint
  where the final approach course of a T approach meets the crossbar of
  the T. When designated (in conjunction with a TAA) this waypoint will
  be used as an IAWP when approaching the airport from certain
  directions, and as an IFWP when beginning the approach from another
  IAWP.
  
  INTERMEDIATE APPROACH SEGMENT [ICAO]− That segment of an instrument
  approach procedure between either the intermediate approach fix and
  the final approach fix or point, or between the end of a reversal,
  race track or dead reckoning track procedure and the final approach
  fix or point, as appropriate.


The Instrument Flying Handbook warns that, “Randomly joining an approach at an intermediate fix does not ensure terrain clearance."

On other approaches, there may not be an intermediate fix, but the segment is defined as follows:


  INTERMEDIATE FIX− The fix that identifies the beginning of the
  intermediate approach segment of an instrument approach procedure. The
  fix is not normally identified on the instrument approach chart as an
  intermediate fix (IF).
  
  INITIAL APPROACH SEGMENT [ICAO]− That segment of an instrument
  approach procedure between the initial approach fix and the
  intermediate approach fix or, where applicable, the final approach fix
  or point.


The Instrument Flying Handbook also talks about intermediate fixes where there is sometimes a charted Intermediate Fix:

Teardrop Procedure


  When a teardrop procedure turn is depicted and a course reversal is
  required, unless otherwise authorized by ATC, this type of procedure
  must be executed. [Figure 1-15] The teardrop procedure consists of
  departure from an IAF on the published outbound course followed by a
  turn toward and intercepting the inbound course at or prior to the
  intermediate fix or point. Its purpose is to permit an aircraft to
  reverse direction and lose considerable altitude within reasonably
  limited airspace. Where no fix is available to mark the beginning of
  the intermediate segment, it shall be assumed to commence at a point
  10 NM prior to the FAF. When the facility is located on the airport,
  an aircraft is considered to be on final approach upon completion of
  the penetration turn. However, the final approach segment begins on
  the final approach course 10 NM from the facility.


Holding in Lieu of Procedure Turn


  A holding pattern in lieu of a procedure turn may be specified for
  course reversal in some procedures.  In such cases, the holding
  pattern is established over an intermediate fix (IF) or a FAF.