Aragorn (Viggo Mortensen) is a lot older than he looks in The Lord of the Rings trilogy. The movies made it a point that Aragorn would never to be able to experience the eternal life enjoyed by Elves. Aragorn's morality was brought up by Elrond (Hugo Weaving) in The Lord of the Rings: The Two Towers when he reminded Arwen (Liv Tyler) that Aragorn would die before her, because she was an Elf and he was just a Man. While it's true that Men don't share the immortality of Elves, some do live extraordinarily long lives in the world of J.R.R. Tolkien.
Despite Elrond's warning, things turned out rather well for Aragorn. Following Sauron's defeat and the fall of Mordor at the end of The Return of the King, Aragorn marries Arwen and becomes the High King of Arnor and Gondor. Aragorn founds the Reunited Kingdom, and under his reign it becomes the most powerful force in the northwest region of Middle-earth. Aragorn ends up living a good life, and not just as a king. With Arwen - who willingly gave up her immortality - Aragorn has one son and at least two daughters. Aragorn's story comes to an end when he dies of old age.
So exactly how old is Aragorn during The Lord of the Rings? As confirmed by Aragorn himself in the movie, he's 87 years old. His reign as the High King lasts for 122 years, which ends with his death at the age of 210. There's an explanation for why a mortal like Aragorn could live for two centuries; he's a member of the Dúnedain, a race of humans called the "Men of the West". The Dúnedain are descendants of the ancient people known as the Númenóreans.
The royal blood that flows through the veins of the Dúnedain allows them to live three times as long as normal Men. Aragorn's heritage is the reason for his longevity, and he's not the only Lord of the Rings character to benefit from being one of the Dúnedain. Faramir (David Wenham), for instance, carries the blood of the Dunedain, which is why he's able to live to the age of 120.
The Dunedain aren't nearly as long-lived as Elves, of course, but they do get experience much more than most Men. Since Aragorn was 87 years old in the movies, the character was old enough to live through quite a bit while with the Rangers of the North. Aragorn participated in several large-scale battles, and traveled through various regions of Middle-earth. What Aragorn's age in means for his character is that he lived a long life full of adventure before The Lord of the Rings story even began.