Then from 5,000 throats and more there rose a lusty yell; It rumbled through the valley, it rattled in the dell; It knocked upon the mountain and recoiled upon the flat, For Casey, mighty Casey, was advancing to the bat.
Here's the short version: the crowd cheered super-loud because Casey was coming to home plate (the place where the batter stands to hit).
Those "5,000 throats" belong to the spectators. Using a part of something to represent the whole (like throats to represent whole people) is what's called in the poetry biz synecdoche.
A few fans might have left (see stanza 2) but there's still a healthy crowd on hand and they are making quite a racket. It's a "lusty yell." No—it's not that kind of lusty. In this context, "lusty" just means strong and enthusiastic.
How loud was it? Well, the sound of that cheering crowd was so loud that it echoed "through the valley."
What's a "dell," you ask? A dell is basically another, more literary, term for a small valley. Remember the "Farmer in the Dell" from your younger years? It's like that. Dell is just a little more poetic-sounding than valley.
In addition to all that valley-echoing, the sound also echoed through "the mountains" and "the flat." It reached near and far, the highlands, the lowlands, and everywhere in between—as we said before: super-loud.
You might have noticed that those descriptive words—"rumbled," "rattled," and "recoiled"—all start with R. Those repeated initial sounds are known as alliteration. This repetition makes the R sound more intense, builds it up, mirroring the way the crowd noise is building. (Check out "Sound Check" for more on this technique.)
To recap: Casey is coming to the plate. There are two outs, and there are two runners on base. Casey has a chance to win the game for the home team (if he can make it around the bases and back to home plate) and those Mudville fans are going wild.