He might get URL info, he may only get IP address info. There is no easy way for any of us to know.
BUT, you have a "political" problem, not a technical one. You need to bring this problem to the adults. Your brother should be removed from admin access, and the router have new factory firmware installed, and factory reset to clear any possibilities of malicious use.
There is a wide variety of information he could be getting, like maestro said, he could just be bluffing and messing with you. If he is actually getting this info, it would more than likely be URLs and IP addresses, which would mean that he is able to view what sites you've been visiting, and potentially what you've been doing at those sites.
I think this is a pretty solid possibility, if you have administrative access to the router it's not hard to set up some parental monitoring controls that view this kind of information. Personally, it sounds like a breach of privacy to me, and I would have a few words with him if I were you.
even when there are multiple devices connected, he knows which one is mine and he knows for example that i'm watching youtube videos. and i can't do anything, he pays for the net and he's very annoying. i just use wifi to pass time when im bored. but since u mentioned that he can get my passwords, that's messed up.. is there anyway to hide my activity and keep my privacy safe?
he can only get everything if he knows how to
its posssible he doesnt know how to get your passwords etc
yes even with multiple devices connected he could identify yours by telling the router to be always assigning them the same ip
or by your mac address
basically you are at the mercy of who ever controls the router
though likewise he is also a target since he is on the same network as you
though i am not advocating striking back at him as things might get out of hand
If your brother is paying for the internet service, you are in essence a "guest" on his network, and he can set the rules. Short of working something out with him where he agrees not to monitor your activity, or getting your own internet service, you are kind of stuck with the situation.
If you are sending traffic over his router, then he can potentially read into that information. Like everyone is saying, you have to know how to utilize that information, but he will have access. Your options would be to setup a VPN or a proxy, but both of those processes are rather involved, can potentially cost money, and probably won't work with a lot of the sites you visit.
The router being under his ownership changes things, you are a guest on his network, and therefore he has full control over your activity on the network, as he should. If it really bothers you, either talk to him and come to an agreement, drop your devices off of his network, or pay for your own. As a guest, you have no control whatsoever over his equipment, and if you can't come to an agreement with him, then just either deal with it, or buy your own.
Start looking at gay porn, let him confront you on that Other then that there's not much you can do, all internet traffic goes out through a single point of the house, if he's monitoring that then there's not much you can do.
If you pay for a VPN service from your laptop/desktop you can basically totally obscure your traffic from him and from your router. He will be able to see that you've initiated a VPN connection, but all traffic between you and the VPN (including the actual destination - not just the VPN server) would then be encrypted and inaccessible to your brother.
I agree with others that this is actually a family/relationship problem, not a technical one. But subscribing to a VPN service like TunnelBear or HideMe (there are loads of others) will achieve what you want it to.