Oversimplified, since OP asked for a simple explanation:
QM deterministically describes the time evolution of a system which is not a model for "the observed universe" but for "all possible universes". (In reality that's not quite right for any particular real-world problem you look at, because it's already been simplified down to a minimal closed-system model that's tractable, but the concept still makes sense to talk about.)
Unfortunately (from the standpoint of someone who wants to use a model to make predictions) there's no way to measure or even approximate the "state of all possible universes" at a given time, and even if you could somehow do that to run the evolution as a simulation, your results would only tell you about all possible universes, not the real world you live in.
So with this in mind, in order to use that to make meaningful predictions, you have to interpret what are essentially conditional probabilities, conditioned on observations: given that I measured [something] at time $t_0$, the chance of finding [some other measurement] in [some neighborhood/interval] at time $t_1$ is [some probability].