What will happen if I sync my iphone to new computer?

I just plugged in my iphone into a new computer and I want to sync my music from my new computer to my iphone. All the music that I had on my old computer is now all transferred to the new computer. When I try to "sync" the music from my itunes library from the new computer onto my iphone a message pops up saying that my iphone can only be synced with one itunes library (meaning the one from my old computer) and if i sync it with the itunes library from my new computer it'll erase my content on the iphone and replace it with the content from the new computer. I'm aware of all this, and I DO have all the stuff I wanted from my old computer already transferred to my new computer, but my question is, if I do allow it to replace the old content with the new content (from the new computer), what exactly happens? I heard that songs can be "overwritten" but what does this exactly mean? If I have the songs replaced does that mean they are "overwritten"? And if so, will my replaced songs or "overwritten" material be able to still play on my iphone AS WELL AS my itunes library? Please explain so I can understand, thank you.

Added (1). @Jack - ok… But that didn't exactly answer my questions about "overwritten", etc…

1 Connect your iPod to your computer with the USB cable that came with your iPod.
2 Open iTunes. Your iPod should appear under Devices in the bar to the left.
3 Change any song information, such as title or artist, in the iTunes library and it will appear this way on your iPod. You can also add album artwork to songs or an entire album. Make sure your iPod can display album artwork before doing this.
4 Click on the iPod icon in the bar to the left and select Sync in the lower right corner.
5 Wait as the songs are added to your iPod.
6 Eject your iPod by clicking the button in iTunes.
7 Unplug your iPod.
8 Listen to your new songs