We are constantly reminded of the fact that the knight is getting older. In the first stanza, he has "journeyed long" (4), which implies that he's already old. Then the speaker flat out says "but he grew old "(7). Then, in the third stanza, we learn that his strength has "failed him" (14), at which point he meets a ghost-like figure. It's not clear if the knight just gets old because he gets old, or because his endless searching has prematurely aged the poor dude.
Line 4: We learn the knight "had journeyed long." The word "journeyed" refers both to the knight's literal journeys, but may also be a metaphor for his journey through life.
Lines 7-8: The knight "grew old" at some point during his search—or maybe as a direct result of his search.
Lines 9-10: The shadow that falls over the knight's heart is a metaphor for the knight's depression or unhappiness, or it may also be a metaphor for his advancing age. Think of it like this: there are more shadows when it's closer to evening, and the knight is clearly in the twilight of his life. The repetition of the beginning H ("his heart") and F sounds ("Fell", "found") is called alliteration.
Lines 13-14: At last, the knight's strength has "failed him." His body is weakening with his advancing age. The repetition of the beginning H sounds here ("his," "him") is known as alliteration.
Line 15: The knight encountered a "pilgrim shadow," which sounds like a ghost to us. This is probably because he was old and close to death—the time when some people claim to start seeing dead people.