Why do we have to strictly focus on something to really see what it looks like? Is everything else around blurred, or is our brain trained only to see in the center of the image projected on the retina?
I basically agree with @Nick Stauner, but I want to add another important aspect, namely the gradient of photoreceptor densities in the human retina: In the fovea there is a sharp peak in cone density compared to more eccentric regions, as described in Curcio et al. (1990) and see the following graph obtained from Web Vision:
The cones have a different retinal circuitry, as about 20-100 cones converge onto one ganglion cell via bipolar cells (Webvision. In contrast, tens of thousands of rods may connect onto a single ganglion cell through massive convergence of rod input into bipolar cells and amacrine cell connections (Webvision). This, together with the exceptional high density of cones in the fovea result in excellent visual acuity in the central field of view, and far lower acuity more eccentrically. Indeed, eccentric vision is used for movement detection and rod-driven night vision (conditions of low lighting), while central vision is used for tasks where high-acuity is preferred (analysis of fine spatial detail such as reading).
Basically, the retina contains two different kinds of receptors: rods and cones. Cones are concentrated in the fovea and activate ganglion cells more discretely than rods. Rods are more interconnected by horizontal cells (if I'm not mistaken...), so multiple rods can often activate the same ganglion cell, whereas each cone is more likely to have its own ganglion cell. Ganglion cells transmit visual sensory input to the brain, so information that is consolidated into one before transmission can't really be discriminated by the brain as coming from one rod or another if both rods connect to the same ganglion cell. Since cones have more independent ganglion cells, they transmit info to the brain more individually. Where cones are concentrated (the focal area of the retina), the resolution of visual perception is more fine-grained.
Here's a somewhat simplistic illustration:
Note the single ganglion cell connected to all three rods, and the three separate cells for each cone.