In the TV series Gotham, other than giving her a vaguely cat-like silhouette do the green-tinted goggles that Cat wears serve any purpose? I've been binge-watching the series (I'm up to episode 9) and so far I haven't seen her wear the goggles over her eyes.
As far as we know, they don't do anything goggles don't normally do. Since we have seen her jumping from rooftop to rooftop, it is likely they may protect her from windblown dirt and bugs but not much else. They are likely an homage to this comic version of the character:
As far as we know, they don't do anything out of the ordinary. The costume designer said that they gave her the goggles to add a modernised steampunk aesthetic to Selina's look. So far, I don't believe we've actually seen her with the goggles on her eyes; they're always on her head, so their probably just there to look very, very cool. I have this fancy that they might be night-vision goggles, though, that enable her to see in complete blackness, just like a cat. The probably also have a protective function, to shield her eyes from wind and dirt and what have you when she's running away from the police.