The Protestant Reformation started in October 31st, 1517 when Martin Luther posted the 95 Theses in his objection to the Roman Catholic Church. Luther, John Wycliffe, John Calvin and those reformers who stood against the Catholic Church became known as ‘Protestants’. In the same way as a ‘defendant’ is one who defends and a ‘contestant’ is one who contests, so a Protestant protests.
As part of the Reformation, five phrases (the solae) evolved to basically lay out the core beliefs of the rebel-rousing protestant reformers. The Latin word ‘sola’ means ‘only’ or ‘alone’ in English.
English: ‘By Scripture alone.’
Basically, this is the belief that the Bible has supreme authority over any and all questions. It does not mean that the Bible will necessarily say something about everything- for example, space travel and stem cells aren’t mentioned anywhere in the Bible, but it does mean that everything we need can be found in scripture.
This contrasts with the concepts such as church traditions having spiritual authority, or a present-day prophet having final say on spiritual matters.
Catholic counter-argument is the Bible does not claim to be the only guide for faith.
See 2 Timothy 3:16 and 2 Thessalonians 2:15.
English: ‘By faith alone.’
Justification with God is accomplished by solely faith, without any need for works. Note that Protestants believe that works will accompany faith, but that the works are not necessary for justification with God.
Wikipedia summarizes this very well:
Protestant: Faith yields justification and good works.
Catholic: Faith and good works yield justification.
Catholic reasoning comes from James 2:14-17, Protestant from Ephesians 2:8-9 and John 3:16.
English: ‘By grace alone.’
This means that salvation is an un-earned gift from God through His Grace. We are saved by God’s Grace and not through our works. Basically Ephesians 2:8, Romans 3:23-24 and Ephesians 1:7.
English: ‘Christ alone.’
There is no salvation though anyone or anything other than Jesus Christ, and He is the sole mediator between God and man. Mary and other saints are honored by holding them in high regard, but they hold no place in one’s salvation or in mediation with God. See 1 Timothy 2:5.
This also gets into the concept of the ‘priesthood of all believers’ and rejects the idea that certain church sacraments must be performed by a ‘priest’. The basis for the ‘priesthood of all believers’ is 1 Peter 2:9 (See also Revelation 1:9 and Revelation 5:10). Note that there are certainly distinctions in the New Testament in various church offices, this speaks more to sacraments such as Holy Communion and confession and intermediary roles.
Soli Deo Gloria
English: ‘Glory to God alone.’
God deserves all the glory, not canonized saints, popes, or other human beings, or angels. This does not mean that good people should not be held in high regard, or that their good deeds go unnoticed, but these things should be done not for the glory of the person, but that through glorifying the person who glorifies God, God is therefore glorified.