Genver is from Latin Ianuarius, meaning the month of Janus – the Roman god of transitions, often portrayed as having two faces, one looking back and one looking forward.
Whevrel is from Latin Februarius, meaning the month of Februus – the Roman god of purification. 'Whevrer' is a reconstructed early form that is unattested in historical Cornish.
Merth is from Latin Martius, meaning the month of Mars – the Roman god of war, and originally a god of agriculture. 'Meurth' is a reconstructed early form that is unattested in historical Cornish.
Ebrel is from Latin Aprilis – probably related to Latin aperire ‘to open’ (referring to blossom, flowers), but also associated with the Greek Aphrodite, goddess of love.
Mê is from Maia – the Greek goddess who came to be associated with the Roman Bona Dea, the goddess of fertility.
Metheven is from Brythonic *Mediosaminos, meaning ‘of midsummer’ (compare hav from *samos), because the summer solstice falls in this month. Efen is a clipped form.
Gortheren is a reworking of original Gorefen (also found) meaning the month after June (gor- ‘over’).
Est is ultimately from Latin Augustus, the title given by the Roman senate to the first emperor, who was born in this month.
Gwydngala is a transparent formation meaning the time of harvest ‘when the straw is pale’ (compare Welsh Medi related to Cornish mejy).
Hedra (Hydref in Welsh) is probably a compound of what is still retained in Welsh as hydd ‘stag’ (Cornish carow) and Welsh bref ‘bleating’, referring to the rutting season of deer (and evidence that Cornish brivya should not be confined to sheep).
Du is transparently ‘black, dark’ referring to the failing of the light.
Kevardhu is prefix kev (intensification) + ar (upon, added to – related to wàr) + du indicating the month when the light is at its dimmest (i.e. the month in which the winter solstice falls).
A note on grammatical usage
All the Cornish names for months may be used adjectivally after mis ‘month’, or as masculine singular nouns in their own right. The resulting phrase with mis is both a masculine noun (like mis itself) and also an adverb. Thus mis Genver means ‘January’ or ‘in January’. It is possible to say in mis Genver but this is rare.