This site is protected as part of a Scheduled Ancient Monument. The County Durham Sites & Monuments Register gives this helpful description:
"A burnt mound is an accumulation of burnt (fire-crazed) stones, ash and charcoal often sited next to a stream or water source. On those examples which have been excavated some form of trough or basin capable of holding water is normally found in close association with the mound. This suggests the stones were heated before being placed into the filled basin to heat up the water either for cooking or has been suggested to produce a sauna like effect within a temporary structure such as a leather tent erected over the basin. Burnt mounds are thought to originate and have their main use in the Bronze-Age. The burnt mound at Foggerthwaite consists of a low charcoal rich earth and stone mound measuring 14 metres north -south and extends 6 metres east from the modern field wall, the mound is a maximum of 0.6 metres high." (sourced from English Heritage, Schedule of Ancient Monumments, 2001, Ref MPP23 AA 11125/1)
The SMR also lists the following doubtful burnt mound at the same map reference (please note that SMR map references are four, not six, digits):
"A very slight mound with some charcoal and burnt stone in mole heaps a few meters north of the linear earthwork forming part of SM343556. The mound is very slight and is mainly visible as an area of dark mole hills, c.5m diameter, at the east end of a slight ridge. Not entirely convincing as a burnt mound, but several other good sites exist in the area." (sourced from Gledhill T & Nichol R, Upper Teasdale backround information file: PRN 6425, MPP Archive, 2000)
No further clue is given, at least in the online SMR, as to what the "linear earthwork" might be, though the "several other good sites" and the Scheduled Monument of which the Foggerthwaite Burnt Mound is a part are no doubt references to the site of Eggleston Stone Circle (now destroyed).