For Protestants wishing to return to Biblical Christianity, the Five Solas became something like a battle cry. Sola Scriptura (Scripture Alone) is the foundational authority for doctrine and the Christian life. And this points to a gospel of Sola Gratia (Grace Alone) effected through Sola Fide (Faith Alone) and by means of Solus Christus (Christ Alone). This brings us to the final element - Soli Deo Gloria, to God alone be the glory.
This must be understood in opposition to a Roman Catholic theology that had effectively put the Church above the gospel and even God Himself. The Church of course is the means through which God works, but after centuries of decline and doctrinal distortion, the Roman Church had become an end in itself, a colossal institution and even an international power. It was (and some argue still is) a counterfeit, the seat of Antichrist - as all the Reformers testified. Through man-made rites and rituals, idolatrous worship of the saints, and through its veneration of the papacy, Rome had not only corrupted the gospel, but stolen a glory that rightly only belongs to God Himself.The Roman system was not only powerful but exceedingly proud. Further, all of its contrived exercises connected to piety (such as the rosary, Lenten fasts etc.) became occasions for self-focus, self-satisfaction, and boasting. There's a real temptation in what Paul calls 'self-imposed religion' or 'will-worship' (Colossians 2:20-23) and Christ (quoting Isaiah) reminds us that it is futile to worship God according to the commandments of men (Matthew 15:9).
God is approached on His terms and the glory in salvation is His (Isaiah 42:8, John 4:24, Ephesians 2:8-10).
How humbling this is to the pride of man! The concept of Soli Deo Gloria also touches on another doctrinal aspect and debate present at the time of the Reformation and it's one that's still with us today - the question of free will and salvation. Roman theology had over the centuries put great stock in man's intellectual ability and the role of reason and philosophy. Man could effectively through his own intellectual prowess reason his way to God and thus revelation and the gospel. The gospel was gracious to be sure and God receives the glory, but man plays a part and thus (by implication) can claim some credit. People debate this and even today get quickly lost in the weeds.
The Reformers believed in Divine Sovereignty in the realm of salvation. God saves, regenerates, and preserves - He even chooses. He alone receives the glory in salvation. We have nothing to offer, nothing to bring - no merit as Rome has taught and continues to teach. On that note, Rome even teaches there's a super-abundance of merit stored up - a treasury built up by the saints that the Church can dispense as it pleases through the sacraments. This is clearly a distortion of the gospel.
Many Protestants would later break with these doctrines taught by Luther, Calvin, and others, once again putting great stock in man's ability and the part he plays in salvation. It must be admitted that the subject is complicated and the debates have not always been helpful. Good men can disagree and some who argue against the Reformer's view are not motivated by pride or a desire to glorify man (in contrast to Soli Deo Gloria), but believe they are accurately reflecting Biblical teaching. They are careful and concerned to make sure that man is responsible for his acts and deeds.
This touches on the nature of doctrine and theology, as well as the role of logic and reason. At the very least let us agree that salvation is of God and while we are held to account for our actions, it is God who saves us, who preserves us to that end, and it is He who is worthy of all honor and glory. This is what the Reformers sought to recapture with the Solas of the Reformation. The gospel had been lost and the Solas represent a way to remind us of central truths that point to the gospel of Grace, revealed in Christ, to the glory of God.