Deterministic models describe behaviour on the basis of some physical law. For example, the planets move around the sun according to Newton's laws and their position can be predicted with great accuracy well into the future. In practice, a totally deterministic relationship is unlikely due to unpredictable factors - for example, a previously unknown comet moving through the solar system could perturb some planets.
Where the influence of several unknown factors is sizable, exact prediction is not possible, but it may be possible to predict to within a known confidence interval - or to predict the probability that a particular value will be observed at a particular time. This is called a stochastic (or probabilistic) process.
A time series is a sample outcome from a stochastic process.