Lines 1-5 are addressed to a young woman (a "maiden") grieving for her "lover," a soldier who has died in battle. Like all the other stanzas in the poem, this one uses a rhetorical device called apostrophe: it addresses someone (or something) who isn't literally present or isn't actually expected to respond.
The speaker tells the maiden not to "weep," adding the suspicious claim that "war is kind." The evidence the speaker provides for this claim is equally suspicious: that the soldier fell off his frightened horse ("affrighted steed") during a battle, flailing toward the sky as the horse ran on without him:
Most likely, the soldier fell because he was wounded. Another possibility is that he simply took a (painful, dangerous) tumble when his horse got spooked. Either way, this isn't really proof of war's "kindness": it's proof of war's cruelty. Note how the assonance of "wild"/"sky"/"affrighted" adds punchy emphasis to the poem's description of a jarring moment.
The speaker's language and logic here are strained and bizarre ("Because your lover [fell off a horse in battle ... ] Do not weep"), yet the speaker asserts that "War is kind" as if no further evidence is needed. What the speaker is saying is so clearly untrue that the poem immediately establishes a sense of irony. Whether or not the speaker truly believes these absurd claims, the poet believes the opposite. Crane trusts the reader to understand the ironic gap between his speaker's words and his own meaning—a gap that will continue throughout the poem.
While the repetition of "Do not weep" and "war is kind" might sound reassuring on the surface, it's in fact disturbing. It's as though the speaker is trying to pressure or lull the maiden into believing something that can't be true. These phrases also establish a refrain that will repeat at the end of the third and fifth stanzas (and appear in line 12 as well).
Finally, the terms "maiden" and "lover" are also interesting: they raise the possibility that the woman and the soldier were unmarried. ("Maiden" usually referred to an unmarried young woman, and a husband isn't typically referred to as a "lover.") If so, they had a baby (see line 12) out of wedlock: a situation that, in Crane's 19th-century America, would likely cause added financial stress and/or social scandal for the widowed mother; unmarried mothers in Crane's society were often treated as outcasts. (Crane tackled subjects such as poverty, social outcast status, and "abandoned" women in some of his other work, including the novel Maggie: A Girl of the Streets.)
In that case, this "maiden" may have more than one reason to weep. Then again, Crane might just be using a word often applied to young women in older poetry, such as the ballad tradition that "War Is Kind" draws on.