I was taught species was determined by whether reproduction was possible. But that was many years ago and I know science changes over time.
That's a workable definition. It does have some seemingly surprising consequences.
For example, two men would not be of the "same" species as they cannot reproduce; some tap dancing with the definition can fix this though.
Another example is having a set of groups of entities such group A can interbreed with B and B with C but A cannot interbreed with C. (This has been observed often in plants and sometimes in animals.) By the definition, A&B are the same species as are B&C but A&C are not. Specieshood isn't transitive. Note that were B to become extinct, A&C would just be different. The chain could be quite long (A,B,C,D,E,F....Z) with interbreeding of neighbors but not at a distance.
The above groups could be distributed in time as well as in geography. For example, and earlier B could interbreed with a later A and with a later C but A anc C may not interbreed. Thus A and C have a common ancestor but are not of the same species.