The first and last letters of the Greek alphabet (Α and Ω). As a title, "Alpha and Omega" is a literary merism — naming two extremes to denote totality ("I know every letter of this story"). The title appears three times in Revelation, always on divine lips (Rev 1:8, 21:6, 22:13), and it is paired in each case with equivalents: "the first and the last," "the beginning and the end."
Alpha and Omega is a claim of unique divine sovereignty over all history. God was before history started (Alpha) and stands beyond its finish (Omega); He speaks the opening word of Genesis and the final "Come, Lord Jesus" of Revelation. Critically, both the Father (Rev 1:8) and the Son (Rev 22:13) use the title of Themselves — a strong Trinitarian datum. In Isaiah 44:6 YHWH declares, "I am the first and I am the last; besides me there is no god." When the risen Christ applies the same formula to Himself, He is not flattering Himself — He is identifying as YHWH. For believers the title is comfort: the Christ who called you is the Christ who will keep you; the story has one author from first syllable to last.