An additional link is any connection between stations that is not a rail link. Either a 'walk', 'tube', 'metro', or 'transfer'.
The way the reservation systems find routes is to do timetable lookups and glue them together as needed with 'additional links'. If a route using an additional link is faster than the through rail journey, it will offer that.
For example
ADDITIONAL LINK: WALK BETWEEN MDB AND MDE IN 10 MINUTES
Hence:
http://ojp.nationalrail.co.uk/service/timesandfares/MDE/EFL/tomorrow/1430/dep
Note that the Minimum Connection Time at MDB is 2 minutes, and therefore the time allowed is 10 + 2 = 12 minutes
Having found the fastest route, it will only then price up tickets.
In the case of MDE - EFL, the ticket is routed Any Permitted, so the shortest route and tickets up to a certain margin longer (~3 miles) is valid. The shortest route is calculated using an internal database, and is via Otford and Sevenoaks and around
The shortest route for MDE-EFL is never shown by NRE, because it is always slower, but it does form the basis (along with easements and mapped routes) for calculating whether the through fare is valid for NRE's calculated fastest route, which happens to include a walk and is far shorter than the shortest route, so is therefore valid.
Some stations, such as Coatbridge Sunnyside-Central do not have fixed links in the database, and therefore, even though they are close to each other, enquiry systems will never suggest walking between them.
The concept of a permitted walk is not one that officially exists, but it does operate in practice for this reason. Actual validity is therefore something of a grey area.
The additional links are not a patch for free-for-all travel, but rather a necessary means of connecting various bits of rail infrastructure without sending people all round the houses.
There are some patches in central London, which is that the various London terminals have mileage connecting them in the database, even though no track exists on the ground. This prevents a lot of 'shortest route' loopholes. Similar mileage patches could be added for Maidstone, Hertford, Dorking et al , to prevent shortest route loopholes around these areas, but at present they only exist in London, albeit even in London undocumented to the ticket buying public.