Dean brings his little sister to the town meeting, even though he has never been to a meeting on his own, and town meetings don’t seem like something a little girl would enjoy as an outing (they probably aren’t suitable for little girls either, as Taylor tells us that the insults bandied around by disgruntled townsfolk can sometimes be pretty adult-oriented).
The only reason Dean has to attend the meeting is to see (stalk, spy on) Rory, and the only reason he has to bring Clara with him is so that she can confirm that the girl who came to door was definitely Rory – he already saw Rory running away, but only from the back. Clara already said she recognised Rory from photos Dean had in his room, so this is to make completely sure before he takes any action.
It all works out as Dean hoped: Rory is at the meeting with Lorelai and Max, and even stands up and makes a speech about how it’s hard to express your true feelings without looking like an idiot. The speech appears to be targeted specifically at him (it is), so that Dean knows that Rory did return his feelings, but was unable to tell him. To seal the deal, Clara identifies Rory as the girl who came to their house, so he knows that Rory has come looking for him, and she’s been stalking him too.