why is there a road link (A38) between Mansfield and Liskeard?

Answer 1

so you can go to cornwall on your holidays

Answer 2

Most of the road started as a lot of local roads, linking nearby towns and villages. However, some of it was built by the Romans to link their forts and settlements.
Over time, some of these roads became more important than others, and became our trunk roads.
At some point in the last century all the roads were classified and numbered. It just happened that the road from from Bristol to Birmingham could be tracked in both directions beyond those cities, and the natural ending points happened to be Mansfield and Bodmin (not Liskeard). The Bristol to Birmingham section is less important now that the M5 exists, but the A38 is still called the Bristol Road just south of Birmingham city centre.
Parts of the A38 run along the route of the Roman

Some other roads can be traced for many miles - particularly the A41 and A5 (both of which have Roman sections - the A5 is Watling Street for the majority of its length), the A1 (parts of which pre-date the Romans) and the A34 but none are as long as the A38.