The poem begins with an apostrophe to "bugles," trumpet-like instruments often used in military ceremonies. In an impassioned exclamation, the speaker urges these instruments to "Blow out," or play their call, "over the rich Dead."
As will soon become clear, these "Dead" are soldiers who have sacrificed their lives in wartime. "The Dead (III)" is part of a sonnet sequence called "1914," written after the outbreak of World War I (1914-1918); the broader sequence establishes that the speaker is an Englishman honoring the UK casualties of that war.
Bugles were once used in combat situations—for example, to signal a call to arms or ceasefire—so it's possible that the poem is set on or near a battlefield strewn with dead soldiers. However, the poem's ceremonious tone makes a funeral or memorial setting more likely.
The speaker stresses that, no matter how humble their background in life, these soldiers are equally glorious in death:
There’s none of these so lonely and poor of old,
But, dying, has made us rarer gifts than gold.
That is, no matter how poor or solitary they were "of old" (in their pre-war lives), these soldiers now belong to a grand company of heroes, who have given their country "gifts" more precious than gold. These gifts fall into two basic categories: the things they've sacrificed (given up), and the benefits their sacrifice has brought. The rest of the first stanza will list items in the first category; the second will cover the second.
Since the poem uses musical imagery (the bugle call) as a framing device, it's no surprise that the language itself is highly musical. The poem is a sonnet and written in iambic pentameter. That means its lines consist of five iambs, poetic feet with an unstressed-stressed beat pattern. This meter features variations here and there to keep things interesting and add emphasis, as in line 1:
Blow out, | you bu- | gles, o- | ver the | rich Dead!
The fourth foot here is a pyrrhic (unstressed-unstressed) while the final foot is a spondee (stressed-stressed). These variations on the iambic meter call readers' attention to the "rich Dead" the poem is honoring. (It's possible to scan the first foot as a spondee too, adding some oomph to the speaker's command to the bugles to "Blow out.")
Finally, these opening lines are packed with alliteration; in line 1, for example, emphatic /b/ sounds ("Blow"/"bugles") mimic the powerful sound of the bugle call itself. In lines 2-3, alliterative phrases ("There's none of these"; "gifts than gold") begin and end the sentence on a harmonious note.