What Does It Mean to Deny Yourself?

Found this quoted by Michael Mckinley at the 9Marks Church Matters blog:

From John Stott's The Cross of Christ, regarding Jesus' statement in Mark 8:34:

To deny ourselves is to behave towards ourselves as Peter did towards Jesus when he denied him three times. The verb is the same (aparneomai). He disowned him, repudiated him, turned his back on him. Self-denial is not denying to ourselves luxuries such as chocolates, cakes, cigarettes and cocktails (although it might include this); it is actually denying or disowning ourselves, renouncing our supposed right to go our own way. ‘To deny oneself is… to turn from the idolatry of self-centeredness.’