So Linux is what Ubuntu is based on?
Sort of. Linux is basically the Linux kernel. All distributions are based on a Linux kernel. The rest, they cobble together various parts, such as desktop environments (KDE or GNOME, among many others), and so forth.
A better analog is Mac OS X and UNIX. Mac OS X is it's own operating system, built off UNIX. There are other operating systems built off UNIX, such as Solaris and BSD.
So Ubuntu is an OS, based on the Linux kernel.
And for convenience's sake, we call all OSes based on the Linux kernel, Linux distributions. Other examples of Linux distros are Fedora, Debian and Mandriva.
Colloquially, yes Ubuntu is Linux.
In other words, if this is more (and hints at much more) than what you want to know, just know that Ubuntu is an OS, and be merry.
On the other hand, if you want to learn more, Google and Wikipedia are your friends.