I noticed this during my third rewatch (I have nothing to do until school starts).
Those are a third eyelid, or scientifically called the nictitating membrane (more commonly called the third eyelid).
In sea creatures, they focus like goggle for humans, allowing them to see clearly underwater. In birds, they serve to clear away debris during high speed flight and protect the eyes while feeding chicks.
Some mammal have full membranes while most (including humans and primates), only have vestigial remnants.
I can’t state if all titans or all titan shifters have this, but Titan Eren certainly does. Given his rage powered healing factor, you may wonder why he would need eye protection if he can just grow them back.
If he were to somehow go to “the continent of ice” or the “fields of sand” in his titan form, he wouldn’t suffer from visibility problems.
It also serves to keep his eyes clean of debris. His regenerative powers won’t keep the residue from a close proximity explosion out of his eyes.