Space itself is getting larger, everywhere, all at once. The scale factor of the universe is getting larger. New space is constantly being "made". Every second, every kilometer in the universe grows by 2.2×10^-18 centimeters. If no other forces were in play, it'd carry everything along with it and pull everything a bit further apart. However, local forces like gravity and the strong and even the weak nuclear force are more than sufficient to hold everything together despite this, so the expansion cannot be locally observed.
That's a small number, but the universe is very big. The hubble constant is usually represented in km/s/Mpsc (kilometers per second per megaparsec), and in those units it comes out to 68. So, every second, every Megaparsec in the universe grows by 68 kilometers. The more parsecs between us and some distant thing, the more space is growing between us and them every second.
For reference, our nearest galactic neighbor is Andromeda, which is 67 kpc away, so about 100 meters of new space is created between our galaxies every second. That being said, Andromeda is heading towards the Milky Way at 110 km/s, so it easily overcomes this and will crash into us any day now^W^W^Win 4.5 billion years.