When I first became a Christian many years ago, I heard words like the one in the title. And then I didn’t any longer. The plain meaning is:

Renunciation or formal rejection of one’s own will; self-sacrifice; unselfishness.

The scriptural basis for the concept is:

Then Jesus told his disciples, “If anyone would come after me, let him deny himself and take up his cross and follow me. Matthew 16:24 English Standard Version (ESV)

And calling the crowd to him with his disciples, he said to them, “If anyone would come after me, let him deny himself and take up his cross and follow me. Mark 8:34 (ESV)

And he said to all, “If anyone would come after me, let him deny himself and take up his cross daily and follow me. Luke 9:23 (ESV)

Of course, you might think of many other verses. What does Calvin comment on Matt 16:24:

If any man will come after me. …The words must be explained in this manner: “If any man would be my disciple, let him follow me by denying himself and taking up his cross, or, let him conform himself to my example.” The meaning is, that none can be reckoned to be the disciples of Christ unless they are true imitators of him, and are willing to pursue the same course.

He lays down a brief rule for our imitation, in order to make us acquainted with the chief points in which he wishes us to resemble him. It consists of two parts, self-denial and a voluntary bearing of the cross.

Let him deny himself. This self-denial is very extensive, and implies that we ought to give up our natural inclinations, and part with all the affections of the flesh, and thus give our consent to be reduced to nothing, provided that God lives and reigns in us.

We know with what blind love men naturally regard themselves, how much they are devoted to themselves, how highly they estimate themselves. But if we desire to enter into the school of Christ, we must begin with that folly to which Paul (1 Corinthians 3:18) exhorts us, becoming fools, that we may be wise; and next we must control and subdue all our affections.

And let him take up his cross. He lays down this injunction, because, though there are common miseries to which the life of men is indiscriminately subjected, yet as God trains his people in a peculiar manner, in order that they may be conformed to the image of his Son, we need not wonder that this rule is strictly addressed to them.

It may be added that, though God lays both on good and bad men the burden of the cross, yet unless they willingly bend their shoulders to it, they are not said to bear the cross; for a wild and refractory horse cannot be said to admit his rider, though he carries him.

The patience of the saints, therefore, consists in bearing willingly the cross which has been laid on them. Luke adds the word daily — let him take up his cross daily — which is very emphatic; for Christ’s meaning is, that there will be no end to our warfare till we leave the world. Let it be the uninterrupted exercise of the godly, that when many afflictions have run their course, they may be prepared to endure fresh afflictions.

John Calvin discusses the reality of self–renunciation in his devotional called An Introduction to the Christian Life, an appendix to his Institutes of the Christian Religion. It is a 44 page tract that begins with a realistic assessment of the difficulties in following Christ and concludes with the very real goals we must aim for if we hope to live the Christian life well. He discusses the middle ground of liberty between asceticism and license (both of which he considers inimical).

So let us:

“Enter by the narrow gate. For the gate is wide and the way is easy that leads to destruction, and those who enter by it are many. For the gate is narrow and the way is hard that leads to life, and those who find it are few. Matthew 7:13-14 (ESV)

Meenikunno Landscape Reserve (the trees are Pinus sylvestris), Ruta Badina, Creative Commons Attribution-Share Alike 3.0 Unported