What does convert higher bit rate songs mean?

Usually. The MP3 default is 128 kbps, however, a lot of the music available for download is lower than this. Unless you ripped the music yourself and chose a higher bit rate your MP3s will be 128 kbps or lower. iTunes music is lossless, so saving to AAC 128 will be a significant reduction in bandwidth, which may or may not be noticeable to the average user. Probably not noticeable to anyone unless you have $1,000 earphones or a high quality external speaker.

Higher bit rate songs are either Apple Lossless format or AAC 256kb/s usually. By converting them you compress their size at the expense of some quality. If you are only listening on cheap headphones there's not reason not to convert. After converting most songs will take up about 1/3 less space. The conversion (which is one time) will take several seconds per song, so if you have a lot of music it can take a long time.

There's no point in converting MP3, however, because its quality is already below AAC 128 kb/s.

So you are saying that the quality of an MP3 file of any bitrate is lower than AAC 128 kb/s?

You are wrong. Most of the music available for download is higher than 128 kbps.

If by "iTunes Music" you mean music from their store, it is lossy, but still high quality (AAC 256 kb/s VBR). "Apple Lossless" is lossless, but is not available from the iTunes store.

If you have "Convert higher bitrate songs to" selected, does it just down convert lossless to lossy (256, 192, 128) AAC or will it down convert higher lossy files, such as 320 mp3, as well?

Does it convert the songs without duplicating them first because my entire iTunes library,at least my music,consists of 1693 songs and has a file size of 8.34 GB,if i choose this option for my old 3rd generation iPod nano,which was my first Apple product,will it copy all of the songs to my iPod directly after converting them,leaving my iTunes Media folder unaffected or does it copy them to my iTunes Media folder first,i had duplicates everywhere and it was a pain to clean them out,i do not want duplicate items scattered everywhere

Does the conversion affect the original file or does it only affect the copy that is synced to the device?

I need to know this too, although I'd assume it would just create a shadow copy at most, storing it locally only for use to transfer to the iOS device. I'd hate for it to create an actual copy to show up in the library, cluttering it all up.