Hi Liquorice,
Gill & Sam are right - a vet visit is definitely needed.
If both eyes have the third eyelid showing it most commonly could be a sign of worms....I know! I didnt know this until my youngests eyes went like that. A trip to the vet confirmed this - she was given a treatment for a common parasite that sometimes isnt killed by the vet prescribed wormer, just incase, as she had not long been wormed anyway.
My 2 oldest cats and my boy who is now at the bridge never had this symptom when worming was due, but perhaps she just felt bit more poorly and under the weather??
On the other end of the scale it could mean a respritory infection - if my memory serves me correctly.
If it is just one eye, it is more than likely an eye infection - but either way a little trip is needed.