This dashing dude rules the fiefdom of Belfalas, which is a possession of Gondor's to the South. Imrahil's castle of Dol Amroth lies on the coast, on the Bay of Belfalas. It is also close to the Haunted Mountain. When Aragorn and the Grey Company emerge from the Paths of the Dead, they come out in Morthond Vale right next to Dol Amroth (though by then, Imrahil has already left for Minas Tirith with his men).
Imrahil is "of high blood, and his folk also, tall men and proud with sea-grey eyes" (5.1.28). He arrives in Minas Tirith along with the other Captains of the Outlands on the first day that Pippin and Gandalf turn up. His men are the best equipped, with "a company of knights in full harness riding grey horses" (5.1.185). There are also seven hundred men at arms, "tall as lords, grey-eyed, dark-haired, singing as they came" (5.1.185). When Legolas first meets Imrahil face to face, he bows to Imrahil because he can see that there is Elvish blood in Imrahil's veins.
Legolas is impressed by Imrahil, and comments, "That is a fair lord and a great captain of men [...] If Gondor has such men still in these days of fading, great must have been its glory in the days of its rising" (5.9.12). In fact, it seems like Imrahil might have some elvish blood to make him stronger than the other guys around him. There is a similarity between the names "Dol Amroth" and "Cerin Amroth," which is the heart of Lothlórien. The people of Amroth (so, the people who once lived where Imrahil is now living) later moved to the Nimrodel River, on the borders of Lothlórien, so there is an ancient link between Imrahil's people and Lothlórien.
Imrahil's banner shows his token, the Ship and the Silver Swan. Since he is a relative of Denethor, he gets to attend Gondor's councils of war. Imrahil leads the troops organized by Denethor to defend the fields of Pelennor when Faramir's retreating troops find themselves attacked by Southrons, orcs, and Nazgûl only about 400 yards from the Minas Tirith city walls.
And it's Imrahil who carries Faramir from the fields of Pelennor back to Denethor with the words, "Your son has returned, lord, after great deeds" (5.4.135). Obviously, Imrahil's words of comfort don't help very much, since Denethor still goes completely insane.
Like the elves Elladan and Elrohir, Imrahil seems like a late addition to Lord of the Rings because Tolkien needs more guys around who can help support Aragorn in battle. Imrahil is the one who keeps emphasizing that Aragorn is king of Gondor, whether Aragorn will take the title during battle or not: "As for me [...] the Lord Aragorn I hold to be my liege-lord, whether he claim it or no. His wish to me is my command" (5.9.74). That means that when it comes down to it, this guy's most important quality is his complete and utter loyalty to Aragorn, whom he backs up right and left.