A good place to start for a high level understanding of all perception and action is Jaoquin Fuster's perception-action cycle. As he says, it's a "cybernetic cycle linking the organism to its environment". He describes two moieties of the brain, posterior sensation moiety, and the anterior behavioral moiety. Information cycles between perception, interpretation (in the posterior moiety), action plans (in the anterior moiety), and actual movement. The movement is perceived, and the cycle continues. This is a good frame for thinking about how saccades work.
Your actual question then is opening a big ol' meaty can of worms. How the brain makes use of the sequence of images produced by the saccades, is actually two questions. First, how does the brain perceive images? Next, how are saccades relevant to this? In the context of the perception-action cycle, we're then looking at how the posterior moiety interprets visual information, and how the anterior moiety acts on that interpretation. Without writing 10,000 words, I'll try and give a thumbnail sketch of this. Then I'll try and circle it back to answer your specific question.
So, how does the brain interpret visual images? Here we only really need to understand that the posterior moiety creates distributed and hierarchical cell assemblies representing increasingly complex sets of features. Distributed because the cell assemblies are sparse, as in they consist of many scattered members each representing a different feature. In some way these are bound together to form the gestalt of the object. Hierarchical because cortical regions are connected in a way where successive regions integrate features from previous regions. So, basically a hierarchical set of cell assemblies are activated and thus the sensory information is represented in the mind.
One point before moving on: these cell assemblies are temporal. They represent information over time. It's not so obvious in vision, but for other sensory modalities it is. What does a single configuration of cochlear activations mean? Or a single configuration of touch sensors? Not much. It means vastly more in temporal sequence. A melody, or a hand patting your shoulder. Vision is not different, the confounding thing is that each individual configuration carries so much information it's easy to think of the visual system as a static system. But it isn't. Saccades themselves are helping create temporal information, by focusing on successive things. If you think in terms of the activity of the retina, instead of the static external scene, you'll see that saccades are an integral part of making visual information temporally dynamic.
Because of this, I don't think it is optimal to think of saccades as a procession of images. On the level of the retina, or V1, this might be true. But throughout the perceptual moiety, these images are bound together. Each saccade doesn't present a radically new image, it elaborates an already existing image within the mind. The higher hierarchical regions are binding the information from each saccade into a framework.
Ok, so if the posterior moiety understands the scene, how is it translated into an action (like a saccade)? I believe the answer is the route through the basal ganglia. The basal ganglia helps "select" motor behaviors. To put it very simply, the perceptual moiety is the input, and the output goes to the anterior motor moiety. Through mechanisms that are unclear, a transform is done where a saccade movement is disinhibited that will move the eyes to the bit of the scene that it wants to see next.
I realize I'm shooting kind of wide here, so let me know if you want to know about something more specific. I'm just not sure that your current question can be answered narrowly.
Fuster, J.M. (1990). Prefrontal cortex and the bridging of temporal
gaps in the Perception-Action Cycle. Annals of the New York Academy of
Science, 608, 318-336.
Felleman, D.J., & Van Essen, D.C. (1991). Distributed Hierarchical
Processing in the Primate Cerebral Cortex. Cerb Cortex, 1, 1-47.
Sakurai, Y. (1999). How do cell assemblies encode information in the
brain? Neuroscience & Biobehavioral Reviews, 23, 785-796.
Engel, A.K., Konig, P., Kreiter, A., Schillen, T.B., & Singer, W.
(1992). Temporal coding in the visual cortex: new vistas on
integration in the nervous system. Trends in Neurosciences, 15,
Hikosaka, O., Takikawa, Y., & Kawagoe, R. (2000). Role of the basal
ganglia in the control of purposive saccadic eye movements. Physiol
Rev, 80, 953-978.