Atticus allows Scout to overhear his conversation with Uncle Jack for two reasons. One, he wants her to understand what is going on with the upcoming trial. Two, he wants her to know that despite being unhappy with her actions, he's proud none-the-less. Allowing Scout to eavesdrop insures she's listening to what he's saying. Let's face it, we often pay more attention to conversations we shouldn't listen to than those we're actually involved in. Atticus used this for his own purpose.
To Kill a Mockingbird