Android OS updates are usually rolled out by the phone manufacturer. In this case it would Motorola. Unless Motorola specifically created an update for the Droid in question, you wouldn't be able to update it to the latest Android OS on your own. For instance, the latest version of Android is Ice Cream Sandwich (Android 4.0). I currently own the first gen. HTC Incredible. I'm not able to upgrade to ICS unless HTC offers an upgrade specifically tailored for my model phone.
The Android OS has had several version updates and in it's wake has created an issue known as "fragmentation", which is the problem you're having. Applications are developed with features available in later versions of the Android OS, which earlier versions can not take advantage of. So you run into older phones not being able to run newer applications. Hope this clears this up a bit.