The statement is ironic because Polonius is known for being long-winded. In this passage, he gives a lengthy speech about brevity—a subject he would have spoken about at length in any other setting.
The statement is ironic because, in Shakespeare’s day, wit was often associated with being verbose. Polonius says that brevity is the soul of wit, but he then goes on to deliver a long monologue that contradicts the value of brevity.
The statement is ironic because, in many cases, being brief can actually be more difficult than being wordy. Polonius is so verbose that it may have been more difficult for him to keep his speech short than it would have been for him to speak at length about the virtues of brevity and wit.
The statement is ironic because it is a very short statement. The fact that Polonius chose this particular sentence as an example of brevity makes his speech even longer than it might have been otherwise if he had chosen another sentence instead!
The statement is ironic because it contradicts Polonius’s usual behavior. It seems like something an intelligent person would do if they were trying to make an argument.