An SSID is just a name you call your access point. For example, if you buy an access point or wireless router from say Linksys, the default SSID will be linksys. You can name yours Sammykins or anything else you want. When you want to connect to an access point, you need to specify the SSID so that the client device knows which AP in the area you want to connect to.

http://www.webopedia.com/TERM/S/SSID.html

And are nonwireless routers able to have an SSID?

Actually, besides having my network connection with the other computers in my house, I am also able to create a wireless network connection, and that won't affect anything, correct?

Only wireless routers have SSID's.