Why can we not see around our point of focus of our eyes? 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).    

References
- Curcio et al. J Comp Neurol 1990; 292:292-523
- Webvision The Organization of the Retina and Visual System, Utah University