*The Universe, as a construction, should be infinite spatially, and finite, chronologically, to the observer. An observer, for example, on Earth, can study the Universe as it is observable: that means, within the confines of the observable limit of that big thing that is the Universe, as a physical entity (even though all light, even back to the time of the Big Bang, is observable, some portions of our 'Verse are so distant, photons cannot travel fast enough to compensate for the increased expansion of our sphere of reality [take a valid, representative, abstract construction of our 'Verse. We're going for an asymptotically flat space-time here, a Lorentzian manifold.** You've got all these photons flying around, fighting against the speed of the expansion of the Universe. Because we've got a roughly infinite amount of space available, the observational limit to the observer is finite, based on the transmission limits of the data involved in making the observation (photons cannot travel with an infinite amount of speed, obviously). So, at a certain point, ****'s so far away, it just doesn't matter. Like, it doesn't truly exist to the observer (us on Earth) because it's too far away to be able to have an effect on our reality. The entire observational action is a bit specific to the observer. The 'sphere of observation' is unique to the observer, that is, two spheres of observation do not necessarily have to overlap. Here's a better explanation. Examples are cool:
“If a particle is moving at a constant velocity in a non-expanding universe free of gravitational fields, any event that occurs in that universe will eventually be observable by the particle, because the forward light cones from these events intersect the particle's world line. On the other hand, if the particle is accelerating, in some situations light cones from some events never intersect the particle's world line. Under these conditions, an apparent horizon is present in the particle's (accelerating) reference frame, representing a boundary beyond which events are unobservable.
For example, this occurs with a uniformly accelerated particle. As the particle accelerates, it approaches, but never reaches, the speed of light with respect to its original reference frame. On the space-time diagram, its path is a hyperbola, which asymptotically approaches a 45 degree line (the path of a light ray). An event whose light cone's edge is this asymptote or is farther away than this asymptote can never be observed by the accelerating particle. In the particle's reference frame, there appears to be a boundary behind it from which no signals can escape (an apparent horizon).” Thanks wiki.
\**a manifold is simply a topological space, of a curved nature, which appears, for all intents and purposes, as a standard, actually flat, Euclidean-space. This is cool, considering flat geometry is a **** load easier to analyze than curved, which involves some really ****ed up math. Manifolds are cool, because it's easy to analyze components of x arbitrary system. A real world example could be something as simple as a 2-sphere (a spherical surface embedded within 3-space, as opposed to a true sphere, which is three dimensional, and incorporates distinct interior and exterior portions). Assume you want to do something like plot the shortest distance from point (x1,y1) to (x2,y2), on that 2-sphere. Well, it certainly is possible to derivate the correct answer using a spherical coordinate system. There are three variables involved: the radial distance, the inclination angle, and the azimuth angle. As well, the inclination angle has to be measured from a fixed zenith. If you're interested, look at a graph. They're cool.
So, it would be very possible to get that exact distance, accounting for the curvature of the surface. It's a lot of computation (think of mathematicians as philosophers. It's so damn hard to sit there cranking out meaningless calculations, while there's important abstract reasoning to be done. Mathematicians are lazy, and dreaming is easier than crunching), for an accurate result. Now, you could do the same thing, but have those points represented on a two-dimensional manifold of that curved sphere, which is really just a 2D plane in standard flat, Euclidean-space. That distance calculation is easy. Remember Rise over Run? Manifolds are cool.