The correct understanding of this term is so fundamental in understanding the reformation. It certainly has nothing to do with linguistics or translations. It has everything to do with the doctrine of justification. There are only two sides to the issue. Catholics (and I believe Eastern Orthodox and the Syrian Churches) do not believe in a momentary or instantaneous justification occurring when we are still God's enemies. They believe in justification as something requiring ‘our cooperation’ with grace (code word for works from a Protestant view) until we are finally justified in the final judgment...based on our ‘cooperation’ with grace. Luther and the reformers thought this was all pure and wicked nonsense. They believed in justification that occurs in a moment, while we have no works but only sin. In other words, while a sinner has no merits, no works (all moral goodness are considered the works of the Law as it is the law that requires them) he is justified forever. No merits whatsoever of any kind only a sinful heart forgiven when a person is made justified in an instant. The only condition is faith but not the active kind, rather the passive reception of a gift, excluding justifying faith as a work also. This has often been called 'an alien righteousness' because it is Christ's righteousness imputed to sinners apart from any of their own internal holiness. It is alien to our inner experience.
In simple terms ‘faith apart from works’ means we are justified in 'a moment' while we have no works to consider at all, i.e. justified apart from anything of the sort. Either we are justified over a period of time, where our obedience and personal holiness and sins are taken into the equation, i.e. ‘justified with works in the equation’, or not. Either it is justified by faith only (apart from any works) or justified with works in the mental equation.
Now this has caused confusion because although in terms of protestant justification our works are not a microscopic part of the equation; yet all who are justified of necessity produce good works as a fruit of the 'alien justification' (i.e. external righteousness of Christ imputed to them). Although 'sanctification' includes the discussion of works and 'cooperation with grace', justification excludes them. Our works having nothing to do with justification at all, but they play a big role in our sanctification. However under the Catholic scheme works are an 'important' part in justification. Actually justification and sanctification are really not much different under the Catholic scheme (i.e. we need continued cooperation with grace in order to be finally justified). Thus Protestants view the Catholic doctrine as works based righteousness hypocritically sprinkled with grace. These two sides should really be clear and do not need any evaluation of Latin or Greek, or German or the invention of different kinds of grace, different kinds of law, etc. Such philosophies only cloud the light of day upon which the Protestant religion was produced. We can’t have it both ways, either our works are considered in 'some sense' in our justification before God, or they are 'not'. One is a classical Protestant view and the other is a Catholic (or Orthodox or Syrian view).
As regards to 'if this is really foundational to Protestantism' the answer is more than anyone probably realizes today.
Just to make it clear that I am accurately representing the reformers on this point I leave a quote from Luther that spells out clearly the difference between those who mix sanctification (i.e. holy love, or works of love) with justification, and those who do not.
The truth of the Gospel is this, that our righteousness comes by faith alone, without the works of the Law. The falsification or corruption of the Gospel is this, that we are justified by faith but not without the works of the Law. The false apostles preached the Gospel, but they did so with this condition attached to it. The scholastics do the same thing in our day. They say that we must believe in Christ and that faith is the foundation of salvation, but they say that this faith does not justify unless it is “formed by love.” This is not the truth of the Gospel; it is falsehood and pretense. The true Gospel, however, is this: Works or love are not the ornament or perfection of faith; but faith itself is a gift of God, a work of God in our hearts, which justifies us because it takes hold of Christ as the Savior. Human reason has the Law as its object. It says to itself: “This I have done; this I have not done.” But faith in its proper function has no other object than Jesus Christ, the Son of God, who was put to death for the sins of the world. It does not look at its love and say: “What have I done? Where have I sinned? What have I deserved?” But it says: “What has Christ done? What has He deserved?” And here the truth of the Gospel gives you the answer: “He has redeemed you from sin, from the devil, and from eternal death.” Therefore faith acknowledges that in this one Person, Jesus Christ, it has the forgiveness of sins and eternal life. Whoever diverts his gaze from this object does not have true faith; he has a phantasy and a vain opinion. He looks away from the promise and at the Law, which terrifies him and drives him to despair.
Therefore what the scholastics have taught about justifying faith “formed by love” is an empty dream. For the faith that takes hold of Christ, the Son of God, and is adorned by Him is the faith that justifies, not a faith that includes love. For if faith is to be sure and firm, it must take hold of nothing but Christ alone; and in the agony and terror of conscience it has nothing else to lean on than this pearl of great value (Matt. 13:45–46). Therefore whoever takes hold of Christ by faith, no matter how terrified by the Law and oppressed by the burden of his sins he may be, has the right to boast that he is righteous (Luther’s works, vol. 26: Lectures on Galatians, 1535, Chapters 1-4.(Vol. 26, pp. 88–89).
Furthermore it should be clear that the reformers, when speaking about 'works of the law' meant moral goodness primarily and not the so called Mosaic legislation (i.e. ceremonies and civil laws). For example, speaking against Thomas who is arguable the emblem of modern Catholic dogma on the subject:
When Thomas and other scholastics speak about the abrogation of the Law, they say that after Christ the civil and ceremonial laws are fatal, and that therefore they have now been abrogated, but not the moral laws. These men do not know what they are saying. When you want to speak about the abrogation of the Law, discuss chiefly the Law in the proper sense of the word—the Law in the spiritual sense. Include the entire Law, without distinguishing between the civil, the ceremonial, and the moral. For when Paul says that through Christ we have been set free from the curse of the Law (Gal. 3:13), he is certainly speaking about the entire Law, and especially about the Moral Law. (Luther’s works, vol. 26: Lectures on Galatians, 1535, Chapters 1-4. (Vol. 26, pp. 446–447)).