I hate to link to Wikipedia here, but given the tendency of many postcolonial theorists to be long-winded and to use academic jargon, this page might be of some help.

Scholars that talk about colonial discourse are generally tapping into a tradition of analysis that goes back to Michel Foucault and Edward Said. They're interested in understanding power relationships, strategies of domination, and the mechanics of colonial rule by looking at what colonizers say and how they say it. What symbols, signs, stories, or arguments are made to serve the colonial project, and how do those ways of speaking impact colonial policy and practice?

The benefit of using discourse as a tool is that it opens a lot of new sources that scholars may not have previously considered meaningful for political histories: literature, song, film, poetry, ethnography, and so on. Those texts can often be very helpful for understanding the cultural output that helped to drive colonial enterprise. The downside of discourse analysis is that it can become circular -- focusing too much on what was said and how than why that discourse is meaningful for how colonialism played out on the ground, in real life.