High Definition is just a n00bified term for high resolution. The color depth isn't any better... The frame rate isn't any better... The only thing that's better is resolution.
480i = 720x480 interlaced
480p = 720x480 progressive
720i = 1280x720 interlaced
720p = 1280x720 progressive
1080i = 1920x1080 interlaced
1080p = 1920x1080 progressive
Most of the time when you see "HD Ready" that means that the device is HDCP compliant. HDCP is a form of DRM/copy protection.
So to answer your question - yes your monitor is capable of displaying high resolution video. It does it all the time, thats all it does is display high resolution video. When you use your computer, your computer is outputing high resolution video. What you are looking at is high resolution video.
If you downloaded some HDTV recordings of TV shows, they will play just fine on your monitor, because all your monitor does is display video all day long at 1440x900.
But it is not "HD Ready" because it is not HDCP compliant, in that it doesn't contain an HDCP decryptor. You won't be able to display an HDTV satellite feed on your monitor unless you're an ub3r l33t hacker who knows a lot about cryptography.