Pre-trained language models for programming languages have shown a powerful ability on processing many Software Engineering (SE) tasks, e.g., program synthesis, code completion, and code search. However, it remains to be seen what is behind their success. Recent studies have examined how pre-trained models can effectively learn syntax information based on Abstract Syntax Trees. In this paper, we figure out what role the self-attention mechanism plays in understanding code syntax and semantics based on AST and static analysis. We focus on a well-known representative code model, CodeBERT, and study how it can learn code syntax and semantics by the self-attention mechanism and Masked Language Modelling (MLM) at the token level. We propose a group of probing tasks to analyze CodeBERT. Based on AST and static analysis, we establish the relationships among the code tokens. First, Our results show that CodeBERT can acquire syntax and semantics knowledge through self-attention and MLM. Second, we demonstrate that the self-attention mechanism pays more attention to dependence-relationship tokens than to other tokens. Different attention heads play different roles in learning code semantics; we show that some of them are weak at encoding code semantics. Different layers have different competencies to represent different code properties. Deep CodeBERT layers can encode the semantic information that requires some complex inference in the code context. More importantly, we show that our analysis is helpful and leverage our conclusions to improve CodeBERT. We show an alternative approach for pre-training models, which makes fully use of the current pre-training strategy, i.e, MLM, to learn code syntax and semantics, instead of combining features from different code data formats, e.g., data-flow, running-time states, and program outputs.