Location-based service (LBS) data are emerging data sources in the transportation domain which contain large-scale, fine-grained, near real-time information in population flow. However, limited studies have built forecasting models based on population flow time series extracted from LBS data. This study introduces a deep learning framework, the Interpretable Hierarchical Transformer (IHTF), for high-dimensional multi-horizontal population flow time series forecasting and interpretation. A variety of cutting-edge deep learning technologies are fused, including the gated residual network to control nonlinearity and to bypass irrelevant information, the variable selection network to assign canonical variable-wise weight, the recurrent positional encoding to learn temporal locality, and the transformer architecture to capture temporal seasonality and trend. Various exogenous variables are included, endowing the framework with sensitivity in socioeconomics, demographics, land development, weather conditions, and holidays. Different internal parameters, such as variable selection weight and temporal attention weight, are extracted to explain underlying patterns learned by the framework. Numerical experiments based on one-year nationwide county-level population flow time series show that: 1) IHTF outperforms extensive baseline models in model accuracy, yielding symmetric mean absolute percentage error (SMAPE) from 8.420% (1-day-ahead) to 11.178% (21-day-ahead). 2) Model performances vary substantially across counties. Large counties broadly present better performances in relative metrics but worse performances in absolute metrics. 3) Feature relative importance generated by IHTF is similar to tree-based model but with more even distribution, among which point-of-interests (POIs) count, county location, median household income, and percentage of accommodation and food services are the most important static variables. 4) Attention weight demonstrates that IHTF can automatically learn trend and seasonality from raw time series. The framework can serve as a dynamic travel demand forecasting module in the transportation planning process. Outcomes can be fed into dynamic traffic assignment to obtain time-dependent link-level traffic conditions in future scenarios.