AMP - 19 [That you may really come] to know [practically, through experience for yourselves] the love of Christ, which far surpasses mere knowledge [without experience]; that you may be filled [through all your being] unto all the fullness of God [may have the richest measure of the divine Presence, and become a body wholly filled and flooded with God Himself]!
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
This is at the end of the second prayer that Paul prays for the Ephesians in this epistle. In both prayers, Paul is concerned with practical, experiential knowledge, not just an academic grasp of doctrine.
Scripture often speaks of the things of God as being "already but not yet." That is, there is one aspect of the truth that is completed right now and we participate in it now while there is another dimension that is future indicating that we only know it in part now.
We know from other Scripture that Christ is the fullness of God. When we are baptized into the body of Christ, we are baptized into him. At that point, and from now on, we are in him and he is in us. Therefore, we have the fullness of God in us in the person of Christ by the power of the Holy Spirit. We may or may not be aware of this reality.
Paul's prayer is that we will come to have experiential knowledge of this fullness of God which we have in Christ.
There is a degree of mystery to what Paul says here. He prays to know the love of Christ that surpasses knowledge. He wants us to know what is unknowable. It can be experienced, but not known academically, apparently. This requires his earlier request that we be strengthened in the inner man to be able to experience this love that surpasses knowledge. It is supernatural, but the key is that Christ is the fullness of God. We need nothing in addition to Christ to have that fullness.