You're using CS3. Select the picture, and choose the "Live Trace" button on the horizontal tool bar on the top of the screen. Play around with the setting, but this will turn the image from a bitmap (rasterized image based on pixels) to a vector image . You can then delete away the parts of the picture you don't need.
Alternatively, you could open that picture in Photoshop, cut out the eagle, save it, then open that image in illustrator, combine it with text or whatever you want.
I don't know if you know this, but I'll tell you anyway: Illustrator is meant to work with vector based images. Vectors are mathematical lines and shapes drawn by the computer that have no (or infinite) resolution. Photoshop deals with bitmap images, like .jpegs, that are comprised of a limited number of pixels, each of which is a certain color and has a limited resolution. Whenever you save a file in Illustrator for the internet, or print it, you have to rasterize it: that is covert it from vectors to pixels, giving it a set resolution.
Illustrator gave you an error message because you had a bitmap image, and Illustrator was looking for vectors to fill with colors. Live trace somehow determines the edges of the image and converts them to vectors that Illustrator can work with.