2 entangled particles are 2 particles whose states are unknown, except that they are linked: e.g. 2 electrons which have opposite spins, or 2 photons which have opposite polarization. So when you measure one particle, you instantly know the state of the other even if it's light-years away (this is not FTL communication as you can't communicate this information FTL).
It's sort of like putting an "up-spin" and "down-spin" electron in a box, having someone shift around the boxes behind your back, putting the boxes far away from each other, and then opening one: before you open the box you have no idea what either box contains, after you open one you know both including the far away one.
Except it's not the same as putting an "up-spin" and "down-spin" electron in a box, because of Bell's Theorem (https://en.wikipedia.org/wiki/Bell%27s_theorem#Theorem). Electrons' spin is actually determined when you measure them: you can measure up/down, but also left/right or any other 3D direction. And if you measure both electrons at a slightly different angle, their measurements probabilistically correlate in a way which means the electrons never really had any true internal "spin" (hidden variable) until you measured one of them. The fact that measuring one electron changes the others' "spin" faster than light seemingly violates the principle of locality.
The part which confuses me in the article is that, once you measure an entangled particle, they are no longer entangled. So I figure in order for this clock to be feasible you would either need an unbelievable amount of entangled atoms, you'd need to instantaneously re-entangle, or you'd need to use a "standard" atomic clock and only break entanglement after a certain number of ticks, to re-synchronize.