Human beings are a people of worship. It may not be God that we worship, but there are many gods which we worship. For some it is money, for others it is family. Many gods and a lot of people feeling empty and longing. We as humanity are looking for a god who will fulfill our lives. Paul encounters the people in Athens who are in a similar pursuit. This is where Paul steps in and claims to know the unknown God.
We know this unknown God as well. The question is not knowledge, rather it is a matter of trust and obedience. The other gods of our lives are often allowed to have rule. We strive and strive for more. money, prestige, importance and more. In the midst we lose sight of the one true God who can offer to us this life we strive for. Interestingly it is not through striving we find this God, it is through submission.
In many ways Paul has a pretty easy task, as we do as well. People are seeking and striving and we know the only source of Truth. It is not ours to convince and argue, it is ours to simply tell the story of the people of God. The rest is in the hands of that very God and the decisions of those seeking to dig into the God who has been made known.