Matthew 16:24

Then said Jesus unto his disciples
Knowing that they had all imbibed the same notion of a temporal kingdom, and were in expectation of worldly riches, honour, and pleasure; he took this opportunity of preaching the doctrine of the cross to them, and of letting them know, that they must prepare for persecutions, sufferings, and death; which they must expect to endure, as well as he, if they would be his disciples:

if any man will come after me:
that is, be a disciple and follower of him, it being usual for the master to go before, and the disciple to follow after him: now let it be who it will, rich or poor, learned or unlearned, young or old, male or female, that have any inclination and desire, or have took up a resolution in the strength of grace, to be a disciple of Christ,

let him deny himself:
let him deny sinful self, ungodliness, and worldly lusts; and part with them, and his former sinful companions, which were as a part of himself: let him deny righteous self, and renounce all his own works of righteousness, in the business of justification and salvation; let him deny himself the pleasures and profits of this world, when in competition with Christ; let him drop and banish all his notions and expectations of an earthly kingdom, and worldly grandeur, and think of nothing but reproach, persecution, and death, for the sake of his Lord and Master: and

take up his cross;
cheerfully receive, and patiently bear, every affliction and evil, however shameful and painful it may be, which is appointed for him, and he is called unto; which is his peculiar cross, as every Christian has his own; to which he should quietly submit, and carry, with an entire resignation to the will of God, in imitation of his Lord:

and follow me;
in the exercise of grace, as humility, zeal, patience, and self-denial; and in the discharge of every duty, moral, or evangelical; and through sufferings and death, to his kingdom and glory. The allusion is, to Christ's bearing his own cross, and Simeon's carrying it after him, which afterwards came to pass.