Going on to the next sentence makes clear the context: the narrator is so nearsighted that he usually needs to use glasses or contact lenses to see properly. When he's at the beach, however, he doesn't like to wear either glasses or contact lenses. Glasses are not mentioned explicitly in the passage you quoted (only in the next sentence), although contact lenses are, but they're there by implication: the "white mask on [his] otherwise tan face" would be caused by wearing glasses so that the tanning effect of the sun would reach all parts of his face except those covered by the glasses. In the next paragraph, his wife finds for him another solution to his sightedness problem, a surprising alternative to glasses and contact lenses: his "seeing hat".
I nearly always saw them at the beach, where it’s difficult to get a good look at anyone. Particularly so in my case, because I’m nearsighted and would rather see everything through a haze than return to Madrid with a kind of white mask on my otherwise tanned face, and I never wear my contact lenses when I go to the beach or the sea, where they might be lost forever. Nevertheless, from the very first moment, I was tempted to rummage around in the bag in which my wife, Luisa, keeps my glasses case—well, the temptation came from her really, because she, if I may put it like this, was constantly transmitting to me the more peculiar activities of the more peculiar bathers around us.
‘Yes, I can see him, but only vaguely, I can’t make out his actual features,’ I would say when she, in an unnecessarily low voice, given the noise level on the beach, would point out some character she found particularly amusing. I would keep screwing up my eyes, reluctant to get my glasses out only to have to return them once more to their hiding place once my curiosity was satisfied. Then one day, Luisa, who knows the strangest and most insignificant things and is always surprising me with scraps of useful knowledge, passed me her straw hat—closer to hand than my hidden glasses since it was on her head—and advised me to look through its mesh. And I discovered that by peering through this screen I could see almost as well as with my contact lenses, more clearly in fact, although my field of vision was greatly reduced.