Best analogy I’ve heard is to imagine our universe was flat and existed on the surface of a balloon. As the balloon expands all 2 dimensional creatures living on the balloon see other galaxies moving away from them. But what is it expanding into? Nothing. Their universe is made of a flat ball of expanding rubber. It’s not expanding into more rubber. There is absolutely nothing that exists within the laws of nature in that 2 dimensional universe that can possibly describe what it is expanding into. In fact it’s really only expanding in time. The balloon was smaller in the past and will be larger in the future. But it isn’t expanding into anything.

Now imagine three dimensions of space and one of time expanding (if you have a better imagination than me) in the same way that balloon expands. It’s not expanding into anything, it is everything and everything is expanding. Also as far as we can tell our universe does not curve into itself like a balloon. Or if it does it must be at least 23 trillion light years in diameter based on the accuracy of our measurements.