My machine is Windows 7. I build my unity scene for the web platform. I click .html file; it says that download unity player. I click on image to download the unity player.
I install unityplayer.exe and run it. I reopen the HTML file; it says that download unity player again.
I don't understand why it doesn't work. How can I install unity player properly?
As Martin mentioned in the comments, Unity Web Player is no longer supported by Unity.
This is because Google announced a plan to deprecate support for NPAPI plugins, such as the Unity Web Player. See the full article here.
I'd suggest switching platforms for your game :-)