Unlike the rest of the town, Miss Maudie is not interested in the "spectacle" of the trial. People are coming out in huge crowds and groups to watch (in Miss Maudie's accurate prediction) "a poor devil on trial for his life."
Her reference to the Roman carnival here is not likely a gladiator-type reference, as many students have observed. The Roman carnival is described a celebration for the sake of celebrating, and it was chaotic. Miss Maudie here does not want to sink to the level of the rest of the town (and surrounding areas) and show a sudden interest in judicial matters simply with the expectation of chaos and entertainment, all at the expense of an actual person's life.
In Chapter 16 of Harper Lee's To Kill a Mockingbird, when the children ask Miss Maudie if she is going to watch Tom Robinson's trial at the courthouse on the day of the trial, Miss Maudie responds with the following:
't's morbid, watching a poor devil on trial for his life.
In saying the above, Miss Maudie is asserting that it is mentally unhealthy, even grisly for people to want to be spectators at a trial, just to see someone being put on trial for his/her life. People who are not Tom Robinson should be feeling enough respect for life itself not to want to watch him be sentenced to death. Later, she tells the children she was certain Atticus would not win the case due to the racial prejudices of the jury; therefore, she knew Robinson would be sentenced to death, which was not something she felt was morally right to observe.
In her response to the children, Miss Maudie compares the spectators heading to the courthouse to attendees of a "Roman carnival" in the following simile:
Look at all those folks, it's like a Roman carnival.
The phrase "Roman carnival" refers to an annual time period of celebration observed by members of the Roman Catholic Church. The period of celebration begins at the feast of Epiphany, which celebrates the Three Wise Men bringing gifts to baby Jesus, and ends at the start of Lent, a period of 40 days of fasting prior to Easter. Carnival time is recognized as a wild time of festivity when all morals are set aside prior to the strict 40-day period of moral observance. The festival is actually rooted in the ancient Roman pagan Saturnalian festival, making carnival time a rather pagan holiday. Hence, in comparing the spectators of the trial to attendees of a "Roman carnival," Miss Maudie is describing the spectators as having an absence of all morals and of behaving rather like pagans than Christians.
In short, Miss Maudie does not want to attend the trial because she feels it is immoral to do so, just as attendees of Roman carnivals have a tendency to behave immorally.