expansion of space
Picture a lump of raisin bread dough rising in the oven. As the dough swells, every raisin drifts away from every other raisin — not because the raisins are moving through the dough, but because the dough itself is growing between them. A raisin far across the loaf recedes faster than a nearby one, simply because there is more dough stretching in between. The expansion of space is this idea applied to the universe: the galaxies are the raisins, and the space between them is steadily growing.
The crucial and surprising part is that galaxies are not flying apart through space like shrapnel from a bomb. Space itself is expanding, carrying the galaxies along with it. There is no centre the explosion came from and no edge it is expanding into — every observer, in every galaxy, sees all the distant galaxies receding from them, and each one would equally think it sat still while the others fled. The expansion stretches the distances between galaxies that are not bound together by gravity; galaxies inside a cluster, your body, the Earth, even our Milky Way are held together by gravity and electromagnetism and do not expand. It is only the wide gulfs between distant, unbound systems that grow.
This single idea reorganises all of cosmology. It explains why distant galaxies recede (Hubble's law), why their light is stretched to redder wavelengths (cosmological redshift), and, run backwards in time, why the universe was once hot, dense, and small (the Big Bang). A common misconception is that the expansion means galaxies are moving through space faster than light is allowed to; in fact, distant enough galaxies recede faster than light, and this breaks no rule, because it is space growing, not anything travelling through space.
Draw dots on a deflated balloon and then inflate it. Every dot moves away from every other dot, and a dot twice as far recedes twice as fast — yet no dot is the centre and the dots themselves never grow. The rubber surface stands in for space, the dots for galaxies.
Galaxies are carried apart by growing space, not flying through fixed space.
Gravitationally bound systems — atoms, you, the Solar System, a galaxy, even a galaxy cluster — do not expand. Only the unbound gaps between distant galaxies grow. The expansion is not pulling you apart.