A section will be signed if a field within it is edited, and that field is marked for signing when saved within a section. Sections aren't really signed at all - the field is - but the client notices the field's inside a section and makes it look like the section was signed. Different sections can be signed by different people.
When saving, Notes will sign all sections to which the user has access - even if signed before by that user or someone else. So, if you want a section signed and that signature to last, you must change the section's access control list to deny permssion to anyone else that might edit the document. Even then, if the signatory edits some other part of the document, the section will get re-signed. To avoid this, it's probably possible to make the section editable by no-one.
Note that the section ACL appears to be just a textlist field in the actual document (i.e. all the section handling is part of the form handling), so permissions can be re-widened (and re-signature etc. re-enabled) from a macro.