For the very beginning, Graves writes about how children are "dumb" to say how hot a day is. But this isn't because they're "dumb" as in stupid. It's because young, young children literally don't have the language skills to describe how hot it is. And based on what comes later in this poem, Graves here is implying that not being able to describe the hot day makes the experience way more intense for little kids. Every hot day is like the first hot day they've ever experienced.
But we have speech, to chill the angry day, (5)
In contrast to kids, we (meaning Graves and his readers) are able to talk about our experiences using "speech." And for some reason, having speech allows us to "chill the angry day." In other words, there's something about being able to talk that makes our experiences less intense. Maybe by talking about the hot day, we're able to think of the day more as a concept than as something that's literally burning our skin and making us all sweaty.
We spell away the soldiers and the fright. (8)
In this instance, Graves actually breaks down language to the level of spelling out individual words. But he does this for the sake of creating a parallel between spelling a word and casting a spell. In this case, he suggests that language has the power to make things seems less scary. For example, if we see a bunch of soldiers walking by, we can make the sight of them less scary by talking to someone about our feelings or by forcing ourselves to be rational about our experience instead of emotional.
There's a cool web of language winds us in, (9)
At this point, Graves makes a direct connection between his theory of language and the "cool web" that he mentions in the poem's title. He basically claims that we humans are caught up in language like flies caught in a spider's web. Language is like a network of words that also exists inside our heads and allows us to relate different experiences to one another according to stuff like themes and concepts. In this sense, we are caught in language to the extent that our experience only "makes sense" if we can put it into words. Anything that can't be expressed in words tends not to count for other people.
But if we let our tongues lose self-possession, Throwing off language and its watery clasp (13-14)
Toward the end of the poem, Graves starts to wonder aloud what would happen if humans were able to leave language behind and to experience the world in a totally unfiltered way. In this sense, we'd be able to throw off the "watery clasp" of language, meaning that language is something that imprisons us.
We shall go mad no doubt and die that way. (18)
But just when Graves starts wondering about how we might liberate our minds and experience the world directly, he ends by claiming that we'd go mad and die if we started experiencing the world with no language at all. After all, we might not even have self-consciousness without language. We'd have no way of making sense of our experience, and we'd probably just lose our minds and die, since we wouldn't be able to take care of ourselves.