What typically occurs during a second interview?

The first interview serves as a screening interview where you typically meet with the screening director in person. This person is often the HR director or could be the person you will be working for directly.
The second interview is also typically a screening interview, where a select few are invited in for a more in-depth evaluation. You will likely meet with the direct supervisor you will ultimately work for, the "team" you will be expected to work with, and other key decision makers who need to be involved with an executive hire (CEO, board or hiring committee).
You may meet individually with several people or even a group who will likely ask you similar questions to your first interview. Make sure to research the individuals you will be meeting with so that you understand their background and perspective on the hire before answering their questions.
The second interview rarely results in an offer session and may not ever cover financial matters, but it will determine whether or not you make it to the third and final interview.