Lets' say, I have built a time series model that can predict daily product sale. Now, for example, time series prediction indicates that sale will drop tomorrow. How can I explain the forecast? Using model, is it possible to know that why sale will drop?
That depends on the type of time series model of your choice. Typical time series models only depend on the time series data and not on external data. That means that they try to describe the structure of the time series. Is it seasonal? Is there a trend? How much noise is there?
These typical time series models (like ARIMA) should thus somehow assume that the time series does not drastically change. It it would, it would ruin their prediction. That's why time series analysis often have the assumption of a stationary processes (see e.g. this chapter of an online textbook "Forecasting: principles and practice" for some visual examples). With this assumption the time series model can safely assume that future exampels follow the same pattern as the past.
Thus for time series models that depend on the stationary process assumption (the majority) the proper thing to say about a prediction is: based on the patterns in the time series I observed in the past, I would expect this increase/decrease tomorrow
"Typical time series models only depend on the time series data and not on external data." is not true unless you have no possible predictors. Time series analysis encompasses the utilization of both deterministic input series and stochastic input series. Additionally analysis can ferret out latent variables such as pulses, level shifts, seasonal pulses and time trends and particular time effects like day-of-the-month , week of the month , lead and lag effects of holiday/special effects. These models are generally referred to as transfer function models and sometimes as dynamic regression models and sometimes polynomial distributed lag models and sometime as autotregressive distributed lag models.