This poem is about the fact that India, at the time of writing, had been colonized by the British Empire. The speaker laments that the country's "glory" days now seem to be only in its past. In lamenting that India's "eagle pinion" is now "chained," he is using metaphor to represent India in the form of an eagle, which once was able to freely coast in the skies, but which is now trapped in the "dust."
The word "pinion" can have several meanings, but in this instance, it refers to the wings of a bird. If the eagle here represents India, then, the image of an eagle—a mighty and powerful bird—with its wings chained down is a vivid and sorrowful one, suggesting a once-great creature whose wings have been unfairly clipped. To chain an eagle down, too, is to go against its nature, preventing it from achieving what it could if others had not intervened. In this sense, India, like the eagle, is a prisoner, brought low by its entrapment.