Dignitas is relatively straightforward. It's more or less akin to a man's honor, the intangible measure of the entitlement to respect that a man might have. One could think of it as being your reputation, or even your family name (except that it's applied to an individual--a family can also have dignitas, however).

Auctoritas generally has a much more political context to it, although it's one that derives from usage rather than being integral to the meaning. Auctoritas also depends heavily on personal reputation and prestige, but rather than being purely a mark of honor and character, auctoritas is a measure of a man's personal opinion. Rather than the official power that magistrates held, auctoritas describes the personal influence that a man commands. For example, each year the order in which senators were permitted to speak, to give their sententiae, was determined, and the guy who was chosen to speak first was the senator who was considered to have the greatest auctoritas. Auctoritas is a description of how willing people are to listen to and follow your advice, because of the weight that your past deeds (which includes offices and whatever) and known reputation lend your opinion--it's linked to dignitas in that actions that will increase the one will usually increase the other (particularly holding public office), but they're not the same.

Mind you, these "definitions" I'm giving you are extremely imprecise. That's partly because of the fact that these concepts are not readily described in English, but also because they're rather nebulous in-and-of themselves--Latin authors, particularly Cicero, are not always 100% consistent with what either means, and really the only way to understand it is to read enough of the texts until you get a real grasp of the concepts