Huh. Does it also have Tweets from people who've followed me (for whatever strange reason)? Cuz I don't know some of those folks. Maybe my cat is using my Twitter, although she has her own account.
It might be retweets. If one of the people you followed is prone to unsuitable/spammy retweets, but you otherwise want to follow them, you can turn off retweets for that person. In the web version, go to their Twitter profile. Click on the little person icon (it's by the button that says "following"). A menu should appear. Click "Turn off Retweets".
You can tell who is sending the retweets by looking under the message. It will say "Retweeted by *person name*". You can click on the name to get to their profile.
Twitter clients may have their own way of handling it, but if not, it won't take long to turn off retweets on a few profiles on the web.