The phrase-slogan sola fide is shorthand for the Latin iustificationem sola fide, justification by faith alone (or, more accurately, justification only by faith), and highlights the main thrust of the concept as a certain singularity in our justification. We are chiefly concerned with the object of the singularity or uniqueness: what is meant by sola?
The Westminster Confession of 1646, developed by reformed theologians, in chapter 11 (Of Justification) paragraphs 1-2, explains:
I. Those whom God effectually calls, He also freely justifies…by imputing the obedience and satisfaction of Christ unto them, they receiving and resting on Him and His righteousness by faith; which faith they have not of themselves, it is the gift of God.
II. Faith, thus receiving and resting on Christ and His righteousness, is the alone instrument of justification: yet is it not alone in the person justified, but is ever accompanied with all other saving graces, and is no dead faith, but works by love. [Underlines added]
They are very cautious to note that the word “alone” (sola) does not in the strict sense refer to “faith” (fides): justifying faith is “not alone”, for it is always with grace, particularly manifested by works of love. This is consistent with the Gospel: no less than two apostles say that faith without love does not justify: James in 2:14-24 speaks of a man whose faith does not work by acts of love, and asks “Can that faith save him?” (v. 14), and Paul in his first letter to the Corinthians (13:2) explains that "if I have all faith, so as to remove mountains, but don’t have love, I am nothing."
Therefore, reformed theologians of this school agree with Catholics that, because justifying faith must necessarily co-operate with love, it is false to apply the word “alone” to it in the strict sense, or to say that a faith that is absolutely and inherently alone, can justify.
What, then, is meant by the word “alone”? Exactly this: the justification is sufficient by itself for the person who is justified, and therefore cannot be added to by our own efforts, for it is God alone Who effects our justification. (This last statement is, however, understood differently by Catholics and reformers, and the two understandings do not coincide: Catholics believe that justification, while we cannot add to it either by faith or by works, nevertheless is attained both by faith and by works. Most reformers understand good works to merely be the fruit of justification.) This is why the phrase iustificationem sola fide places the word sola directly in front of the word “justification” and not “faith”, as it often appears in the English translation. It is not an adjective that describes the faith, but an adverb that modifies the act of justification: we are only justified by faith, just as Paul says in Galatians 5:6, that “only faith working through love” matters to Jesus for our justification. There, the word “only” modifies the act of justification by Christ, to say that His work is sufficient of itself. It does not modify the word “faith”, for Paul immediately says that this faith co-operates with love.
In conclusion: This, then, which we have just explained, is what reformed theologians mean by the phrase-slogan sola fide, and it is consistent with the Catholic faith. The Council of Trent’s anathema to those who profess sola fide does not apply to the reformers of this school, for the anathema was pronounced against “any one [who] saith, that by faith alone the impious is justified; in such wise as to mean, that nothing else is required to co-operate in order to the obtaining the grace of Justification” (Council of Trent, Session 6, Canon 9; underlines added) and as we have seen the Reformers held that justifying faith must co-operate with love.