There are a few types of irony, but the general meaning is when something different from what is expected happens. For example, in Hurst's "The Scarlet Ibis," it is ironic to call a small child who is not projected to live for very long "William Armstrong." Brother compares his little brother's name to "tying a big tail on a small kite," which would also be ironic.
Another example of irony from the story is that a coffin is built for Doodle soon after he is born. Although children do sometimes die as babies, a mother doesn't usually plan on burying a child right after giving birth. Usually, the mother expects to love and rear that child to adulthood. However, another ironic situation occurs when everyone does expect the baby to die, but then he doesn't; consequently, the coffin is stored high in the rafters of the barn until or in case the boy dies.
One major irony, though, if one were to pinpoint one big one, would be what happens after Brother teaches Doodle to walk. No adult or doctor thought Doodle would ever walk, but he does. During the summer before Doodle enters elementary school, though, Brother expects to teach his little brother to run and play like other kids at school so he won't be embarrassed.
"School was only a few weeks away, and Doodle was far behind schedule. He could barely clear the ground when climbing up a rope of vines, and his swimming was certainly not passable. We decided to double our efforts, to make that last drive and reach our pot of gold."
At this point, Brother fully expects Doodle to learn how to run since he also knows how to walk. Brother also thinks that he is helping his little brother. But in the process of all their hard work and physical training, Brother winds up pushing Doodle too hard, and Doodle dies while trying to please his big brother.
Thus, throughout the story, Doodle exceeds everyone's expectations by doing such things as living longer than anticipated and learning to walk; however, in the end, Brother expects Doodle to become stronger and like other little boys, but he doesn't. Not only that, but it is because of Brother that Doodle dies. This is ironic because there is a time when Brother wants Doodle to die, but when he gets to the point that he wants his little brother to live, it is then that Doodle dies. Doodle probably would have lived longer had he not been pushed too hard physically.
Therefore, there are many smaller moments of irony throughout the story such as Doodle accomplishing the unexpected over and over again. But when Brother expects too much more, the result is tragic--and that's ironic, too.