First a simple one.
Imagine all the counting numbers: 0, 1, 2, 3, 4, … Imagine counting like this forever. Let's call this type of infinity countable infinity.
Now imagine all the digital information ever. All the books, films, digitized music. All the content on the internet, and on every hard drive.
Imagine our civilization living forever, digitizing all of our art and knowledge, our communications, all our documentations of life, generation after generation. Let's call this digital infinity.
Imagine the infinity of instants in a single breath. Every moment of lived consciousness that passes from the beginning of an inhale to the end of an exhale. Call this breathed infinity.
Now imagine every instant of time ever. Imagine that time never ends and goes on forever. Imagine that the past also never ends, and stretches behind us forever. Think of all the moments of time, forever into the past and forever into the future. Call this eternal infinity.
Finally, imagine the vast expanse of the universe. Imagine that it goes on forever in every direction -- up, down, left, right, forward, backwards. Imagine every place in this space, and imagine every moment in every place. Think of every event that ever happened or might happen, in the past and future, anywhere in this space. Let's call this universe infinity.