I can summarize "Casey at the Bat" for you; for a summary of "The Highwayman," try submitting another question tomorrow, as the format of this website allows for one question a day.
"Casey at the Bat" is a classic and well-loved baseball poem. It is about a baseball game, where one team is down. In fact, in a town called Mudville, Thayer states, "The Outlook wasn't brilliant for the Mudville nine that day," setting up a scene where the Mudville team has 2 outs in the last inning, and they were 2 behind. The crowed is discouraged; in fact, "A straggling few got up to go in deep despair" to leave because they had no hope for their team. The fans pin all of their hopes on a player named Casey, who apparently has a good batting record and who they feel can save the game. But, two players are up before him, who they don't have hope in. To everyone's surprise, the two players before Casey get on base, on 2nd and 3rd, so there is hope of winning when Casey steps up. But, Casey lets 2 strikes go by him because ""That ain't my style," said Casey.'" He's waiting for a better pitch. The crowd, infuriated, yells at the umpire, crying fraud, but Casey calms them down. Then, for the last pitch:
"They saw his face grow stern and cold, they saw his muscles strain, And they knew that Casey wouldn't let that ball go by again...
Oh, somewhere in this favored land the sun is shining bright;
The band is playing somewhere, and somewhere hearts are light,
And somewhere men are laughing, and somewhere children shout;
But there is no joy in Mudville - mighty Casey has struck out."
So, the poem ends with Thayer have set up all of our expectations for Casey to blow the ball out of the park, but, in reality, he strikes out. It's a great poem, that has a really cool ending that surprises the reader and makes for a good chuckle. I hope that those thoughts help; if you haven't read the poem yourself, give it a go. It's an easy read, and very entertaining.