Why would a reaction favor one isotope over another?
Chemically speaking compounds containing isotopes are very similar but not exactly similar

Broadly when compounds contain different isotopes of the same element (say different isotopes of oxygen) their reactivity is the same. But this is a little over broad. There are subtle and (usually) small differences and these can show up as small differences in chemical reactivity.

To get an idea why consider the simple physical properties of water and heavy water. In heavy water the two hydrogens are replaced by deuterium (hydrogen with an extra neutron in the nucleus). A heavy water molecule is about 10% heavier than a normal water molecule (molecular mass ~20 rather than ~18). As a result the physical properties are a little different: bp is about 2°C higher, mp about 4°C higher and the liquid is about 10% denser. So careful techniques can separate the two (by repeated fractional distillation, for example). 

The slight differences also appear in chemical reactions. The reasons why are more complex than the explanation of simple physical effects. But one hint that they exist is simply that the vibrational frequency of a bond depends on the mass of the atoms making up the bond. Isotopes have different masses so there will be some difference with different isotopes. And bonds vibrating are part of the mechanism of reactions involving that bond so the reactions will have different rates. The detailed theory is pretty complex (see this) and the size of the effect depends on the detailed mechanism of the reaction. 

Reaction rates for some reactions involving bonds to hydrogen can differ by large factors (because deuterium is twice as heavy as hydrogen) and are sometimes 10 fold. Most other isotopes have only small relative mass differences compared to their parent element and the net rate differences are often only small single-digit percentages. This results in some reactions concentrating some isotopes over others (eg 18O vs 16O. But these can be large enough to detect by mass spectroscopy.

So, despite their chemical similarity, some reactions and some physical processes will favour one isotope over another (though often only very slightly). If you understand the key reaction mechanism, the small differences in the concentrations can tell something about the conditions of the reaction (temperature dependence, for example).