...but the universe is quite big, getting bigger and even accelerating. It took me a long time to learn to accept this concept. A friend reminded me a while ago of my own troubles with it. He asked me, "if the universe is expanding, what's it expanding into." I don't put a question mark on it because I don't think he really intended it as a question so much as a statement. I believe that because when I replied, "I'm not entirely sure it's expanding into anything", he got angry with me. It is, however, a valid question so long as it ends in a question mark. For a long time during my college education I spent evenings asking myself the question but then not having the question mark at the end myself.
Before going on, I would point out because only recently I learned, a priori means before gathering evidence (at least that's what it means to physicists).
Scientifically, I don't know that the question neccesarily has meaning. I also don't know that the question doesn't. Let's say, for argument, the entirety of existance at this given slice of time occupies a finite volume. Scratch that. I can't use the word occupies. Let me start over. Let's say, for argument, the entirety of existance at this given slice in time has finite dimension. That's better. I'm asuming less that way. (This is how physicists think by the way. We're always tyring to get rid of unneccesary assumptions.) Now I am talking about all of existance. If there were something outside of it, that wouldn't make sense because I am talking about all of existance. A priori, there is no reason for me to think that all of existance must be infinite. I have no experience measuring the entirety of existance and so I can make no natural assumption about that. Let's then just say it isn't infinite for the sake of argument.
Is there then a problem with that finite dimension changing as we move forward in time? This is generally where the question arises. If it's getting smaller, then where did the missing parts go? If it's getting bigger, then where did it get the new parts? This is, however, a very human view of time being used in this way of thinking. To our normal lives, time is different than space. I can measure the length of something spacially with a measuring tape. I cannot so measure the length of something in time. This yields a very common-sense (and very practical) view of time as something intrinsically different than space.
I am not going to tell you this view of time is wrong. However, I will also not tell you this view of time is correct. I have no experience divining the nature of time versus space and, a priori, I can't decide whether they are the same or different. Let us then say for the sake of argument that time is not different than space but rather our different methods of measuring space and time are artifacts of some other part of physics. If time and space are intrinsically the same, this changes how one interprets the idea of the universe getting larger or smaller in time.
Imagine in your mind a cone pointing downward. Imagine then that I take a series of slices of that cone perpindicular to your view. In other words, each slice is a very clean circle. As I move up the cone, the circles are getting larger. Let's say that cone is the universe. All existance is this cone. More importantly though, rather than a three dimensional cone, it's a four-dimensional cone. In four dimensions, a cone is defined as three-dimensional spheres getting linearly larger as you move along the fourth dimension. What I have described is a universe which is getting bigger without having to rely on it expanding into anything. If time is no longer special, then the universe can grow in time the same way the radius of a cone grows as you move along a given dimension. It is not growing into anything, but rather the universe is of a certain shape, and our choice of time is artificial.
A priori I don't know whether time is different than space or not. A priori I don't know if space is finite or infinite. However, there seems to be a combination of these possibilities that allows for an expanding universe in which the universe does not have to expand into anything. This is my understanding of what some people who study this particular phenomenon are saying. I hope you find my description helps you understand what these people are saying.