Crop yield forecasting plays a significant role in addressing growing concerns about food security and guiding decision-making for policymakers and farmers. When deep learning is employed, understanding the learning and decision-making processes of the models, as well as their interaction with the input data, is crucial for establishing trust in the models and gaining insight into their reliability. In this study, we focus on the task of crop yield prediction, specifically for soybean, wheat, and rapeseed crops in Argentina, Uruguay, and Germany. Our goal is to develop and explain predictive models for these crops, using a large dataset of satellite images, additional data modalities, and crop yield maps. We employ a long short-term memory network and investigate the impact of using different temporal samplings of the satellite data and the benefit of adding more relevant modalities. For model explainability, we utilize feature attribution methods to quantify input feature contributions, identify critical growth stages, analyze yield variability at the field level, and explain less accurate predictions. The modeling results show an improvement when adding more modalities or using all available instances of satellite data. The explainability results reveal distinct feature importance patterns for each crop and region. We further found that the most influential growth stages on the prediction are dependent on the temporal sampling of the input data. We demonstrated how these critical growth stages, which hold significant agronomic value, closely align with the existing literature in agronomy and crop development biology.