Is the universe infinite in size? Well, it's really effing huge, that's for sure, but can something really be infinite? Plus, we know it's growing, and if it was already infinite, how could it grow more? But if the universe isn't infinite, what's outside of it? And we're just talking about the universe as it stands right now. What happens when you add space-time into the equation? Plus there's some evidence that there may be a multiverse, how do we account for that?
Those are all some phenomenally weighty questions, whether you're discussing them with an astrophysicist or with your friend that really likes reefer. The answers are equally heavy, but this video from Minute Physics does an admirable job of explaining them. One of the most fascinating aspects of how we define the universe is the difference between the observable universe–the universe from our perspective–versus the universe as a whole.
The observable universe is limited by time, space, and our own perspective, but that perspective is growing all the time. Meanwhile, the universe as a whole likely had a temporal beginning, but is also likely spatially infinite. But can we be sure? Not presently, no. Still, science is more about finding the right question to ask than finding definitive answer, and in that, the video does an admirable job of explaining what we know about the universe at this point in time. Still, should multiverses be real, expect everything we know to go out the window.