Most accurate radiometric dating method
We call the original, unstable isotope (Uranium) the "parent", and the product of decay (Lead) the "daughter".
From careful physics and chemistry experiments, we know that parents turn into daughters at a very consistent, predictable rate.
We have dated meteorites using Rb-Sr, Sm-Nd, Pb-Pb, Re-Os, and Lu-Hf isotope systems and have obtained very similar ages.
The fact that the age we calculate is reproducible for these different systems is significant.
This is why crystals are good for radiometric dating: the atoms in a crystal are extremely efficiently packed, and it's very difficult to get anything into a crystal such as a contaminant by any means short of destroying the crystal and re-growing it anew.
When an unstable Uranium (U) isotope decays, it turns into an isotope of the element Lead (Pb).The ratio of the parent to daughter then can be used to back-calculate the age of that rock. The reason we know that radiometric dating works so well is because we can use several different isotope systems (for example, Uranium-Lead, Lutetium-Halfnium, Potassium-Argon) on the same rock, and they all come up with the same age.This gives geologists great confidence that the method correctly determines when that rock formed.Because geochronologists want to measure isotopes with different masses, a mass spectrometer works really well for dating things.I do think that radiometric dating is an accurate way to date the earth, although I am a geochronologist so I have my biases.