The first thing the seal does is provide authenticity for the letters sender. Each important person or official would have their own engraved picture or emblem on the stamp or ring. So to get a letter with that impression in the sealing wax would provide proof that the letter was indeed from the person claiming to send it and not a forgery. Of course that does assume that the person receiving the letter recognized the senders seal, otherwise it meant nothing.
The second service provided by the seal was a guarantee that the letter had not been tampered with. If someone opened and read the letter while in transit the seal would be broken and the recipient would then know that someone else had read the letter and knew of its contents, as well as potentially tampering with the message of the letter.
Paul uses this image of the seal in Ephesians to describe a part of what the Holy Spirit does in the life of a believer
When you believed, you were marked in him with a seal, the promised Holy Spirit, who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession—to the praise of his glory. - Ephesians 1:13b-14 NIVIn this passage the Holy Spirit is the seal of God stamped onto all those who have believed. The Holy Spirit within is proof to me that I belong to God. And his presence should be a demonstration to other believers as well that I am God's. But for those who are not themselves sealed by the Holy Spirit, the seal on our lives, like the unknown wax seal, has no value; to them there is no possible proof of God's ownership.
In the Ephesian passage the seal is not so much a guarantee that the contents have not been tampered with as it is a promise guaranteeing the inheritance of those who are sealed. If I know the Holy Spirit's presence in my life, I can rest assured that my future with God is secure. The Holy Spirit's presence is the first deposit on that life, with the remainder coming at my redemption.
This sealing by the Holy Spirit is one of the spiritual blessings that Paul has been sharing, and one that I am very grateful for. With the Holy Spirit sealing my life, I do not have to live in doubt concerning my eternity. Instead, I can rest assured that God will provide, and I praise him for that.