I'm trying to give a short answer:
Static analysis looks at the syntactical structure of code and draws conclusions about the program behavior. These conclusions must not always be correct.
A typical example of static analysis is data flow analysis, where you compute sets like used, read, write for every statement. This will help to find e.g. uninitialized values.
You can also analyze the code regarding code-patterns. This way, these tools can be used to check if you are complying to a specific coding standard. A prominent coding standard example is MISRA. This coding standard is used for safety critical systems and avoids problematic constructs in C. This way you can already say a lot about the robustness of your applications against memory leaks, dangling pointers, etc.
Dynamic analysis is not looking at the syntax only, but takes state information into account. In symbolic execution, you are adding assumptions about the possible values of all variables to the statements.
The most expensive and powerful method of dynamic analysis is model checking, where you really look at all possible execution states of the system. You can think of a model checked system as a system that is tested with 100% coverage - but there are of course a lot of practical problems that prevent real systems to be checked that way.
These methods are very powerful, and you can gain a lot from the static code analysis tools especially when combined with a good coding standard.
A feature my software team found really impressive is e.g. that it will tell you in C++ when a class with virtual methods does not have a virtual destructor. Easy to check in fact, but really helpful.
The commercial tools are very expensive, but worth the money, once you learned how to use them. A typical problem in the beginning is that you will get a lot of false alarms, and don't know where to look for the real problem.
Note that nowadays g++ has some of this stuff already built-in, and that you can use something like pclint which is free.
Sorry - this is already getting quite long...hope it's interesting.
