Symbolism, Imagery, Allegory
If you don't catch the hints earlier in the work (check out Aslan's analysis in the "Characters" section more on this), you will have better luck seeing Aslan's symbolic nature when he raises King Caspian from the dead at the end of the work. In that final scene on the mountain, Lewis carefully inserts images from stories connected to the life of Christ so that we can understand the role he means for Aslan to play in this work.
So when Aslan weeps over Caspian's dead body (just as Jesus weeps over the death of his beloved Lazarus), or when he asks Eustace to drive a thorn into his paw and uses the blood to raise Caspian from the dead (Jesus' blood is the ticket to remaining with him forever, too), we know that Lewis wants us to make the connections between these two figures.
But while Lewis wants us to make connections, before he died, he insisted that the Chronicles of Narnia is not an allegory. Instead, he wanted us to see Aslan as a kind of "thought-experiment" or what he called a "supposal." In 1958, Lewis wrote this in a letter to a woman called Mrs. Hook:
If Aslan represented [God], he would be an allegorical figure. In reality however he is an invention giving an imaginary answer to the question, "What might Christ become like if there really were a world like Narnia and He chose to be incarnate and die and rise again in that world as He actually has done in ours?" This is not allegory at all. (Source)
While it seems like a really hard distinction to make, Lewis is actually trying to make it easier on us (is it working for you?)—he's basically telling us not to work so hard. So while Aslan can and should be identified with Christ, we shouldn't try to stretch the comparison so far that it muddies up our view of the fantasy world around him.