Jesus calls himself "the Alpha and the Omega"1; the beginning and the end. This is a cornerstone of Christianity; that Jesus Christ is part of the Godhead (second Person of the Trinity), has existed since before the Creation, and will continue to live eternally.
It is worth noting that long before Christianity, Judaism had a similar way to describe the eternal nature of God. In Exodus 34:6 (KJV), Moses "proclaimed, The LORD, The LORD God, merciful and gracious, longsuffering, and abundant in goodness and truth".
When describing the attributes of God, those words have a profoundly deeper meaning than when we bandy them about in general conversation. The oath: "I promise to speak the truth, the whole truth, and nothing but the truth" (sometimes preceded by "I swear by Almighty God"), is often very far from the truth; as the number of perjury cases confirm.
In contrast, God's truth is perfection and the Hebrew for truth is (Emeth), which is composed of three letters: Thaw, Mem and Aleph (reading from right to left). The letters Aleph the Thaw are the first and last letters of the Hebrew alphabet, so the first and last letters of God's truth are similarly the beginning and the end. There was nothing before God and there will be nothing after God, since God is eternal.
(Don't try to understand the 'beginning' or 'end' of eternity - you'll just give yourself a headache.2)
As Sean Wright kindly pointed out to us, ΑΩ often appear together with other symbols. On the left are two variations of the Chi Rho Cross, Chi and Rho being the monogram of Jesus Christ. So by adding 'Christ' to the 'beginning and end', we have a combined symbol which gives us an acronym of the complete phrase: "I am the Alpha and Omega."
It has become a popular monogram which appears on many items; rings, vestments, etc., and even tattoos, with dubious regard for the symbol's real meaning: the Divinity of Jesus Christ.
No surprise therefore, that ΑΩ also appear frequently with Christian crosses and other symbols to represent the Divinity of Christ.
For example, the emblems of the Associate Reformed Presbyterian Church (ARP), Baptist Community in Central Africa (Communaute Baptiste au Centre de l'Afrique: CBCA), Kalimantan Evangelical Church (Gereja Kalimantan Evangelis: GKE), Presbyterian Church in Cameroon (PCCa), and the United Church of Canada (UCC).
The coat-of-arms of the Anglican Diocese of Trinidad and Tobago (ADTT) also includes the shield of the Trinity, since "Trinidad" is the Spanish word for "Trinity"3 and more importantly, it reflects the basis of Anglican theology.
Another fine example appears on the coat of arms of the Spanish Principality of Asturias. This mountainous area on the northern coast of Spain is traditionally linked to the Spanish crown. It boasts being the earliest Christian political entity to be established in the Iberian peninsula and remained a Christian stronghold when most of Spain entered its 700-year Islamic period from the 8th century.
The persistence of Christianity in this region makes the selection of the Alpha and Omega in their coat of arms particularly significant. Christ, the beginning and the end.