Averroes is commenting on a line in Aristotle's De Anima, in which Aristotle says that actual knowledge is identical to the object of that knowledge (De Anima 431a). The meaning of this was disputed by both Muslim and Christian philosophers throughout the medieval period. Most agreed that, at the very least, Aristotle was saying that true knowledge entailed a perfect reflection of the known object being created in the mind, like an image in a mirror. In this sense, the idea is relatively uncontroversial. If the image in your mind does not resemble the object you claim to know, then you do not really know the object at all. Knowing the object perfectly would mean that the image in your mind was identical to the object.
Averroes, however, goes somewhat further than this, saying that there is a direct ontological relationship between the perceiving mind and the object perceived. The precise nature of this relationship is mysterious, but the person who truly knows an object can be said to participate in that object, to "get inside it" in a way that identifies the knower as well as the knowledge with the object. This level of knowledge means that judgments based on it are not merely speculative, but necessary, since they are derived directly from the known object itself.