Early diagnosis and prediction of chronic kidney disease (CKD) progress within a given duration are critical to ensure personalized treatment, which could improve patients' quality of life and prolong survival time. In this study, we explore the intelligibility of machine-learning and deep-learning models on end-stage renal disease (ESRD) prediction, based on readily-accessible clinical and laboratory features of patients suffering from CKD. Eight machine learning models were used to predict whether a patient suffering from CKD would progress to ESRD within three years based on demographics, clinical,and comorbidity information. LASSO, random forest, and XGBoost were used to identify the most significant markers. In addition, we introduced four advanced attribution methods to the deep learning model to enhance model intelligibility. The deep learning model achieved an AUC-ROC of 0.8991, which was significantly higher than that of baseline models. The interpretation generated by deep learning with attribution methods, random forest, and XGBoost was consistent with clinical knowledge, whereas LASSO-based interpretation was inconsistent. Hematuria, proteinuria, potassium, urine albumin to creatinine ratio were positively associated with the progression of CKD, while eGFR and urine creatinine were negatively associated. In conclusion, deep learning with attribution algorithms could identify intelligible features of CKD progression. Our model identified a number of critical, but under-reported features, which may be novel markers for CKD progression. This study provides physicians with solid data-driven evidence for using machine learning for CKD clinical management and treatment.