What does Katniss mean when she says "We all feel a little closer today, don't we?"
Katniss' statement and question helps to illuminate the particular importance of the moment and of the day, in general. She says it at a point early in the novel where she and Gale are out hunting. They hunt together and enjoy the presence of one another's company, something that Gale says represents the only time in which Katniss smiles. Their entire hunting experience is one in which the intimacy between them is deepened:
The food’s wonderful, with the cheese seeping into the warm bread and the berries bursting in our mouths. Everything would be perfect if this really was a holiday, if all the day off meant was roaming the mountains with Gale, hunting for tonight’s supper. But instead we have to be standing in the square at two o’clock waiting for the names to be called out.
They feel "closer" as a recognition of this bond because of the importance of the particular day.
The connection they share is amplified because today is the Reaping. The ceremony in which two youths are chosen to kill or be killed, Katniss and Gale understand the urgency of the moment. It is a subject that neither of them openly discuss, but both know are there. For Gale and Katniss, the implications of the Reaping are particularly large as both have entered multiple times in order to receive bread and oil for their families. Since both of them understand the importance of the day and the impact it can have on their lives, they feel "a little closer today" because of the shared experience.