The Warp Highways theory is an attempt to explain the various occasions when the speeds and distances given in the show do not tally. The TNG TM gives a speed chart which is shown on the notes page you have just come from, but this has been contradicted several times. The list below contains some examples of odd speeds and distances in Trek :
 

• "Star Trek V : The Final Frontier", in which the Enterprise travels from Earth to the centre of the Galaxy during the course of the film. Given that Nimbus III is located "in the neutral zone", it can be an absolute maximum of 8,000 light years from Earth - assuming that Earth is on one extreme of the Federation, Nimbus on the other, and that the Federation was just as big in Kirks day as it is in TNG times. Assuming Earth to be 25,000 light years from the core, then the minimum speed the Enterprise achieved was 2,500 light years per hour, the maximum 4,853 light years per hour - depending on the relative positions of Earth and the Nimbus system. Since we are given the journey time specifically at "present speed", established only moments before as Warp 7, this establishes poritively and canonically that the speed of a given warp factor can vary wildly. This example is the main basis for the warp highways idea.
• TOS, "Bread and Circuses". In another solid example of this type, Chekov reports that planet IV, system 892, is only 1/16 of a parsec away and "we will be there in seconds". Less than 30 seconds of continuous, uncut scene later the ship begins to enter orbit. This speed equates to 215,640 x c - that's TOS Warp Factor 59.97, vastly higher than the ships designed maximum of Warp 8. It's also about equal to the Encyclopedias stated speed for subspace radio, which is TNG Warp Factor 9.9999. Again we have positive canon proof that the ship is capable of travelling much faster than is generally supposed, at least under certain conditions.
• TOS, "That Which Survives", features the Enterprise being knocked 990.7 light years away from the planet. The time to return is unclear, but dialogue between Kirk and co. stranded on the planet indicates that the ship returns within about 36 hours at most. At Warp 8 the trip should take almost two years, indicating a Cochrane factor in the area of about 500.
• Voyager, "The 37's", features Tom Paris telling Amelia Earhart that Warp 9.9 is equivalent to 4 billion miles per second. This translates to over 21,450 times lightspeed. However, according to the Encyclopedia warp speed chart, Warp 9.9 is 3,053 x c. Again, a solid canon statement that the speed of a given warp factor is variable.
• TOS, "The Menagerie"/"The Cage", in which Pike says that he comes from a stellar group "at the other end of the galaxy". This indicates that ships are capable of trans-galactic travel under at least some circumstances. I would suggest that the Nimbus III - Galactic Core highway continued on into the other side of the galaxy and that this was the one used by the Enterprise, if only to keep the number of assumptions down to a minimum.
• TNG, "11001001", features the Enterprise-D facing a warp core breech. With only minutes to go until the ship is destroyed, Data announces that he has set the computer to take it out away from the nearby inhabited star systems. This indicates that he expected the ship to be able to cover a distance of at least several light years in the time remaining, although no specific distances or speed are given.
• TNG, "Where Silence has Lease", features the E-D being trapped in a mysterious 'hole in space'. An opening appears 1.3 parsecs away, and Picard orders the ship to head for it at Warp factor 2. This would give a travel time of some five months, which seems excessive. It is possible that Picard was just being cautious and planned to speed up later, however.
• TNG, "Clues", when the Paxans throw the Enterprise-D a distance of 0.54 Parsecs, Riker comments that it is "nearly a days travel in thirty seconds". At warp six, the ships normal cruising speed, the Enterprise would need 1.6 days to cover the distance. An alternative explanation for this one is that Riker worked the time out for Warp 7, which comes to slightly under 24 hours, but this seems to be an odd choice as it is neither the ships normal or maximum cruise speed. However I would class this one as a possible supporting factor only, rather than positive proof.
• TOS, "Friday's Child". It is stated that a freighter can manage a maximum of warp 2. This should be only 8 x c on the TOS scale, but this would make interstellar travel virtually impossible - crossing even one sector (20 lightyears) would take 2.5 years! While it's theoretically possible that freighters take decades to get from place to place, it does strain credibility. Mine, at least.
• TOS, "The Squire of Gothos". It is established a couple of times in this episode that the Enterprise is 900 light years from Earth. At the normal cruise of Warp 6 this trip would take over four years - most of the Enterprises five year mission time - just to get there from Earth, without any stops. Plus the same time to get back - yet in "The Doomsday Device" just seventeen episodes later, they identify the next star system they will pass through as Rigel. Episodes are typically set two weeks apart, so the two episodes are about eight months apart.

• TNG, "Bloodlines", has Riker stating that it will take the Enterprise-D 20 minutes to travel 300 billion kilometres at Warp 9. This equates to a speed of 833 x c, which is substantially lower than the 1,516 x c figure quoted in the Encyclopedia. This establishes two highly important features of the highways. Firstly, the speed multiplier of a highway can be less than 1, so reducing the ships speed rather than increasing it. Second, they can cover wide areas rather than narrow corridors - else the ship would simply have skipped off to one side to clear the highway and made the trip at its normal speed.