Kenneth Konyndyk defines these two as follows:
Modality de re is modality thought of as applying to a thing (res), more precisely, as a way a thing possesses a property.
For example, one thing might be said to possess a property necessarily, or something can be said to possibly have some given property, as in the claims that Socrates is necessarily rational or Socrates is possibly a sailor.
Modality de dicto is the modality applied to a statement (dictum). It refers to the manner or mode of a statement's being true.
For example, it is necessarily true that all bachelors are unmarried. Here it is the statement (the dictum) that is said to be necessary. More exactly, it is the statement's being true that is necessary. (Introductory Modal Logic, 78-9)
Sometimes it is useful to interpret a proposition either de re or de dicto.
"The number of planets in the Solar system is 9," when interpreted de re, means "It is true of the number which is equal to the number of planets in the Solar system that that number is 9." Since the number of planets in the Solar system is, indeed, 9, the de re reading is a trivial "9 = 9." In order to carry information, our proposition must be read de dicto.
"Agatha believes that the tallest spy is a spy," when considered de dicto, is analytic and self-evidently true. Of course, the tallest spy is a spy! He must be, necessarily. The de re reading, on the contrary, looks like this: "There is an object in the actual world, x, of which Agatha believes something, namely that he is a spy; in addition, perhaps unbeknownst to her, x also happens to be the tallest spy out there." This is much more meaningful.
Consider the statement, "George IV wondered whether the author of Waverley was such-and-such." The de re reading is inappropriate, because it means: "George IV wondered of x which had the properties (1) of existing; (2) of being unique; (3) of having written Waverley, whether x was such-and-such." He may not have realized that x had these properties, though if he did, the de re reading would be equivalent to the de dicto reading.
In the statement "Socrates is necessarily rational" the modal modifier "necessarily" is applied de re, and the statement is true (it is the essence of men to be rational);
in the statement "It is necessary that Socrates is rational" the same modifier is applied de dicto, and the statement is false, because Socrates does not exist in all possible worlds.
On the other hand, "Necessarily, what is seen sitting is sitting" is de dicto and true; "What is seen sitting is sitting necessarily" is de re and false.