My ignorant and probably incredibly flawed analogy is as follows:
Beliefs incur certain actions. If I say to you that I think democracy is the greatest system of governance in history, you might infer from this that I participate in this system with the act of voting. If, when asked if I vote, my response was to say 'nah I don't see any point in it' then you might legitimately question my belief in democracy. It's easy to say we believe things, but our actions betray what we really believe.
Thus, works are the actions that we are called to make as a consequence of our faith. Works are the expression of belief in action. For instance Christ calls us to love our neighbour. If we aren't trying to do this in our actions, and struggling to put it into practise in our lives, how can we say that we really believe in Him?
From a Lutheran POV nothing in this sounds problematic. Indeed I don't think there's anything disagreeable. Luther himself speaks of the impossibility of separating faith from works, because faith does good works, it can't help but do them. What Lutheranism says--and says very strongly--is that the Law (what God commands) is not Gospel, and the Gospel (what God has promised and gives us freely) is not Law. Thus there must always be a firm and hard distinction between the two.
What that means is that we can never attribute saving power to our works, as though the works we do contribute to our standing and place before God; rather our place before God is solely God's work and grace. Which is why we speak of our justification, our righteousness before God, as a passive righteousness, a righteousness that comes from God, given to us as a gift. Specifically it is Christ's righteousness. When it comes to our good works, this is instead understood as an active righteousness, and not a righteousness before God (in order to gain reward or earn favor from Him by our own merit), but the active righteousness before the world.
To put it another way, God isn't the One who needs our good works, it's our neighbor who does. Faith in action through good works isn't to our benefit before God, but for the benefit of others. The reason we should feed the hungry isn't that in doing so God will award us brownie points, or give us extra ticks on the scoreboard to aid us through Judgment and toward life everlasting--but because there are hungry people who need food, and it is God's good command that the hungry be fed, that the poor, the orphan, and the widow be taken care of.
By making this distinction we avoid the pitfall of the Opinio Legis ("Opinion of the Law"), the notion that I can through my own strength, power, and effort attain righteousness and holiness deserving of eternal reward; and instead confess that it is from God alone that we have what we have. That we are, in the nakedness of our sin and mortal flesh beggars before God, and that Christ alone reconciles us to God and unites us together with Himself and thus brings us into communion with Him, His Father, and the Holy Spirit (noting that it isn't Christ alone apart from the Father and the Spirit, but like all things as it pertains to God's works, it is a Trinitarian activity; rather it is Christ alone apart from our fallen and frail efforts and attempts at merit).
Faith alone, in Lutheranism, isn't "Salvation means subscribing to this set of theological propositions and adhering to them by mental assent"; but rather that faith is God's gift through His own gracious activity through the Means of His Word and Sacraments, through which we are given new sight to behold God in Christ, ears to hear God's word and Gospel, new hearts to love the Lord our God. To cleave to Christ, trusting Him, and that it is here in this faith that we are new creatures in Jesus Christ, and thus are justified before God. Which is why Lutheranism says faith is the new birth (in distinction to other theories in which some argue faith precedes regeneration, or those that say regeneration precedes faith).
All of this, obviously, is quite firmly from within the language of the Western theological tradition, hence the language of justification, merit, etc. And there will always be at least some lack of cross traction between the Western and Eastern traditions, simply because our languages of theology are frequently quite different.
-CryptoLutheran