Total Depravity
"The body, the mind, the will, the spirit-indeed, the whole person have been infected by the power of sin." -R.C. Sproul
The doctrine of total depravity defines the Reformed understanding of original sin--the concept that humans are born into a state of fallenness due to Adam's and Eve's first sin in the garden
The word "Total" in "Total Depravity" refers to the total or, whole person. So in that sense, total depravity means that the entirety of a person is impacted by humanity's fall. This fallenness impacts our natural bodies, the way in which we think, and the bondage of our will.
In short, we are born corrupted to our core, meaning we must be transformed from the inside in order to truly conform to the image of Christ. And, this radical change can only be performed in this life by the work of the Holy Spirit, reaching its full completeness upon our glorification in Heaven.
Unconditional Election
"He that perishes chooses to perish; but he that is saved is saved because God has chosen to save him. -Charles Spurgeon
The doctrine of unconditional election the Reformed view of election says that God saves those He chooses to save based on His own sovereign decision and not based on what someone has done or will someday choose to do. God's foreknowledge of our actions is not what drives Him to save or condemn us; this is what makes the election unconditional.
Some people react against this view, saying it is "unfair" for God to choose to save some while not others. This is where the concept of grace the unmerited favor of God plays such a large role. Everyone deserves to perish. Those who are saved receive grace and those who do not receive justice; it's important to note that nobody receives injustice.
Limited Atonement
"But if the first be the case [that Christ died for all the sins of all men], why are not all men free from the punishment due to their sins?"-John Owen
Doctrines of atonement concern the intended effectiveness of Christ's atoning work on the cross. In the case of limited atonement, Christ's sacrifice was specifically intended to save the elect and only the elect. To say the atonement was limited is not to say God's ability to save His people was limited, but rather that the atonement was always intended to be limited to the elect.
This largely centers around the question of the atonement's intent. Was God's plan in Christ's sacrifice simply to make salvation possible or to ensure the salvation of His people? An unlimited atonement reduces the effectiveness of the atonement in that it is only as effective as the number of people--if any--who might choose to accept it.
To be clear, the atoning work of Christ is sufficient for all, but not all who hear the Gospel believe and repent, and only those who believe and repent can benefit from the atonement of Christ, else everyone would already be saved.
Irresistible Grace
"Irresistible grace does not drag the unwilling into the kingdom, it makes the unwilling willing."-John Piper
The Reformed faith believes that regeneration precedes faith and that regeneration is monergistic- regeneration is the work of God alone. This single-handed transformation of our soul is irresistible grace
Because we are dead in our sins, we have no ability to change our own hearts. As such, salvation is something God must do in us, because we would not ask for it otherwise. To be sure, the term irresistible does not mean we are dragged kicking and screaming to Christ; rather, we are regenerated into a state where we actually want to run to Christ, holding nothing back.
Perseverance of the Saints
"It is He, therefore, who makes them to persevere in good, who makes them good. But they who fall and perish have never been in the number of the predestinated."-Augustine
Many people practice the Christian faith in their lifetime, but not all of them stick with it. If they abandon it, were they ever saved to begin with? The Reformed notion of perseverance of the saints is quite simple: if you have a genuine faith and have been blessed with the saving grace of God, you will never lose it; if you lose it, you never had it. Scripture is undeniably clear on this
Still, that doesn't mean that those truly in the faith won't stumble and continue to fall in this life. But for them, the difference is that their perseverence is through Christ and not by their own strength. By the Will of God, they cannot fail; He will not let them.