Analysis is a core skill of business analysts. But what is meant by analysis in this context? Business Analysts do specific types of analysis, such as Business Analysis or Requirements Analysis. But those are the application of a general analytical skill to specific situations, for specific purposes, using often specific methods.
Generally, analysis means “A process of dismantling or separating into constituent elements in order to study the nature, function, or meaning.” Or “… the ability to visualize, articulate, and solve both complex and uncomplicated problems and concepts and make decisions that are sensical based on available information. Such skills include demonstration of the ability to apply logical thinking to gathering and analyzing information, designing and testing solutions to problems, and formulating plans.” 
However, Business Analysts need to analyze problems in more than a deconstructive sense, and need to ensure they are considering the wide range of factors that surround the problem space that may impact the problem solution, but which are not part of the problem itself (such as business priorities, organizational politics, etc). This is where skills like Systems Thinking prove useful.
BA’s need to use both the more traditional methods of analysis (especially when analyzing requirements and business rules) and the systems thinking approach (to understand the context of what they are analyzing, the stakeholders affected, and the impact on the greater business, among other things).
Some specific analytical skill areas are:
- The only way I know to really improve your analytical skills is experience. But if anyone has more suggestions, please let me know and I will add them.