...having your mind's eye1 enlightened in order to perceive2 what is the hope of His invitation3, what is the glorious wealth of His inheritance in the saints and what is the surpassing greatness of His power4 into us, the believing, according to the work of His mighty4 strength4...These verse piggyback on what Paul says in the verse before, about God giving us a spirit of revelation. These two verse begin to describe what that is to be revealing: God's power. Mind you, this is not merely speaking of God's power in general, for it is predicated on Christ's resurrection in the following verses. However, in the meantime, let us consider what this is saying about God's power.
First, we are to perceive the hope of His call. This same language is used again is 4:4. Hope here refers not to the emotion of hope, but to the object of hope: that which is hoped for. This hope is our eschatological hope: eternal life. Furthermore this is a hope to which God invited us. The Greek word can also mean "call", but it is also the word which is used to mean invitation, like to a feast for instance. I believe it is in this sense that it is being used here: We are invited to the marriage feast of the lamb.
Second we are to perceive the glorious wealth of His inheritance. Again, the concept of inheritance is eschatological, and has been a major aspect of discussion within the past few verses. This inheritance is what we have received in Christ, and here Paul is praying that we understand the full depths of that. Our inheritance isn't just eternal life, but is also the subordinate power and authority that we have through Christ. We should not underestimate this.
Finally, we are to perceive surpassing greatness of His power into us. God's power is not some abstract concept that we try to understand, nor is it restricted to what God does in the big picture of things. God's power is exacted onto us, the believing. Because we will believe, God will do the same mighty act that He did on His Son: resurrecting us from the dead and seating us in power over creation.
Since Paul prays for us to understand these things, that it is good for us to seek and understanding of these things. There must be something practically beneficial to it. I would say that it is this: if we understand what God has done for us, then we understand the kind of privilege that we have. This will give us the confidence to live out the authority that He has given us on earth, humility in understanding that this is a gift given by God, but, more importantly, it will keep in our mind a conceptual view of our relationship to God and others.
Remember that Ephesians is a book primarily about unity in the Church. This is the aim. I would say that Paul prays for us to understand these things so that we understand that we are all (both Jew and Gentile) positioned in the same place in relation to God, and should therefore be united. There should be a bond to forms between us as peers of power.
When we look at a brethren, even the one's that we disagree with about certain issues, we should see him/her as a fellow heir in the things of God, and an equal partner is the place of power. Let us, therefore, treat one another with love, dignity, and respect motivated by the mutual understanding we have about God and Christ.
1Literally "eyes of your heart". 'Mind's eye' is a common colloquial expression that means the same thing though. The ancient concept of the heart wasn't so much one's emotional faculties, but where one's person was.
2The Greek is actually the simple word for 'know' ('oida'). I chose to use perceive instead to coincide with the enlighenment metaphor (literally, shine light onto something so that the eyes of your "mind" can see it better).
3 The word 'klesis''s most basic meaning is that of a vocal call: calling out to someone else. However, this is also the common word in the Greek for an invitation. To decide whether to translate it as 'call' or 'invitation' is determined mostly on context. Though I think that 'invitation' is a better translation here, I am aware that this may be bias on my part (though I don't think it is) and accept that criticism.
4'Dunamis', 'kratos', and 'ischus' are all synonyms relating to strength. 'Dunamis' is related the concept of ability, while 'kratos' can also refer to authority. 'Ischus' simply means strength. As such, my only real attempt is to do my best to also use three English metaphors, since this seems to be Paul's rhetoric.