What does it mean to carry our own cross?

The best way to first approach this question is to ask its opposite. What does it not mean? We don't do for ourselves ANYTHING that Jesus did for us when He died for us on the cross. We don't add to His suffering or His sacrifice. We don't cancel or fulfill anything. We don't please God in a saving way. No debts that determine our eternal destiny are paid off. The crosses we carry are ONLY crosses of response to His.

It is symbolism. Unlike Christ, we do not go to death on the cross ourselves, yet death is the point. We are to die to ourselves and our sin, and live to Christ. Look at the fuller context of the verses in Mark 8:31-38...

- He then began to teach them that the Son of Man must suffer many things and be rejected by the elders, chief priests and teachers of the law, and that he must be killed and after three days rise again. 
- He spoke plainly about this, and Peter took him aside and began to rebuke him. 
- But when Jesus turned and looked at his disciples, he rebuked Peter. “Get behind me, Satan!” he said. “You do not have in mind the things of God, but the things of men.” 
- Then he called the crowd to him along with his disciples and said: “If anyone would come after me, he must deny himself and take up his cross and follow me. 
- For whoever wants to save his life will lose it, but whoever loses his life for me and for the gospel will save it. 
- What good is it for a man to gain the whole world, yet forfeit his soul? 
- Or what can a man give in exchange for his soul? 
- If anyone is ashamed of me and my words in this adulterous and sinful generation, the Son of Man will be ashamed of him when he comes in his Father’s glory with the holy angels.”

What do we know here? We do we learn? Here are some thoughts:

1) Suffering is a part of faith on Christ's end and ours. Any faith that minimizes suffering, especially the suffering of Christ, minimizes salvation and, apparently, maximizes Satan.
2) Christians always did and always will have a problem with the Cross. Every human being has the natural desire to put distance between himself or herself and the Cross and what it means.
3) The only way we can keep our souls is through "taking up our cross." This means that we can't live Godly lives until we die to all that is in competition with the Cross.
4) To gain the whole world is not worth much in the long run.
5) If Christ calls us to "take up our cross," or to suffer, then He must also provide the inner means of fulfilling this.
6) Our adulterous and sinful generation, or our culture, can exert a powerful influence over us, making us want to defy even God in order to gain social approval. Part of carrying our cross is resisting this.
7) Being ashamed of the Cross is being ashamed of Christ is being rejected by Christ. You cannot be a Christian of any kind and reject the work of Christ on the Cross
8) That which preserves our lives in eternity may end our lives here.

So what is following Christ, taking up our cross, and losing our lives for Him and the Gospel? It is to live lives above the influence and values of this world and beneath the shadow of the Cross of Christ. It is to live lives where we endure whatever is necessary to endure in order to maintain our fidelity to the Cross of Christ. It is a choice we make every day of our lives.