Not just on Memory Map but all Orgnance Survey Maps...
A black dashed line is: "Other road, drive or track, unfenced" In other words a physical track on the ground but one with no public right of way. If the track is fenced it is shown as two parallel unbroken black lines.
So this shows what is physically
on the ground and is usually a "vehicle width track" (a narrower "path" would be shown as a thinner dashed line) but it doesn't mean you can ride it as this symbol does not show the status
of the track.
You can see them both here http://www.satmap.co.uk/pdf/explorer.pdf
Sometimes both of these can be overlaid by a right of way symbol to show the legal status (footpath, bridleway, restricted byway or byway open to all traffic) or often by the "ORPA" symbol (a series of red dots (1:50,000) or green dots (1:25,000)) showing it is an "Other Route With Public Access" which in the vast majority of cases (but not always) shows that it is an "unclassified County Road". I say not always as the ORPA symbol can also be used for things like paved footpaths in urban areas or cyclepaths (but these are usually obvious on the ground).
DMMO stands for Definitive Map Modification Order. The Definite Map is the record of all Public Rights of Way held by the local Highway Authority (usually County Council) . To change anything on it, e.g. to upgrade or downgrade a right of way to a different status, to divert the route or stop it up altogether, requires a modification order, known more properly as a "Definitive Map Modification Order" or "DMMO".