(Image courtesy of http://lexfridman.com.)
"The Spirit Himself bears witness with our spirit that we are children of God, and if children, then heirs - heirs of God and fellow heirs with Christ, provided we suffer with Him in order that we may also be glorified with Him" (Romans 8:16-17).
"Does Paul tell us why suffering must precede glory? We can give at least part of the answer. It's found in Romans 5:3, 'And not only this, but we also exult in our tribulations, knowing that tribulation brings about perseverance.' There's the clue: Suffering, or tribulation, works endurance or perseverance. Perseverance of what? Faith. How? By knocking the props of self-reliance (and trust in things and people) out from under us, and making us rely more on God (see 2 Corinthians 1:8-9).
If there were no afflictions and difficulties and troubles and pain, our fallen hearts would fall ever more deeply in love with the comforts and securities and pleasures of this world instead of falling more deeply in love with our inheritance beyond this world, namely, God himself. Suffering is appointed for us in this life as a great mercy to keep us from loving this world more than we should and to make us rely on God who raises the dead. 'Through many tribulations we must enter the kingdom of God' (Acts 14:22).

There is no other way. Do not begrudge them. They are hard to bear. I know they are. But if you keep your inheritance before you, and if God gives you the grace to see what Paul calls 'the riches of the glory of his inheritance' (Ephesians 1:18), then will you not say with the apostle, 'I consider that the sufferings of this present time are not worthy to be compared with the glory that is to be revealed to us'?" ("Christians, Heirs, and Fellow Sufferers," John Piper.)

Assuming it is possible to add to what John Piper already said, let me put it this way:
A young lady from a wealthy​, aristocratic family in Boston went away on a long trip to visit her cousin in the hill country of West Virginia. Where once the young lady had been waited on by butlers and maids at breakfast, lunch, and dinner - and, of course, afternoon tea-time - she now assisted her cousin in taking a bucket to the river to retrieve water, plucking the chicken's feathers off the carcass, and hitching up the plow to the mule in order to prepare the field.
​"I wasn't made to live like this," the young lady often said to herself. "My fingernails are covered in dirt, my beautiful yellow dress is filthy, and my hair hasn't been cared for in weeks! I cannot wait to go home and rid myself of this present suffering."
This is what our present sufferings are like. All creation has been subjected to sin and futility; that is, incapable of producing any useful result by itself.​ All creation is incapable of producing a useful result apart from Christ. But Christ has set creation free from the bondage of sin and corruption! "For the creation was subjected to futility, not willing, but because of Him who subjected it, in hope that the creation itself will be set free from its bondage to corruption and obtain the freedom of the glory of the children of God" (Romans 8:20-21).

​And so we suffer, along with all created things, longing for the day when we shall return to our beautiful home in the glory of God - as citizens of heaven because we are heirs with Christ! "For we know that the whole creation has been groaning together in the pains of childbirth until now [when Christ has been revealed]. And not only the creation, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for the adoption as sons, the redemption of our bodies" (Romans 8:22-23).​

​Suffering, therefore, is any result of sin we endure while looking forward to the salvation that will be realized and completed in Christ (Romans 8:24).

​We suffer when we feel the weighty burden of the sin-filled world around us, who passionately pursue death through their sinful lusts.​ We suffer when our bodies break down in sickness and disease. We suffer when we are beaten, slandered, and criticized as a result of trusting in Jesus. We suffer when we ourselves struggle against temptations to sin. In hope, we look forward to the day when our battle with sin will be over (Romans 8:21) and our bodies will be redeemed (Romans 8:23)!

The famous John Newton puts Christian suffering in this manner:
"Suppose a man was going to New York to take possession of a large estate, and his [carriage] should break down a mile before he got to the city, which obliged him to walk the rest of the way; what a fool we should think him, if we saw him ringing his hands, and blubbering out all the remaining mile, "My [carriage] is broken! My [carriage] is broken!" (Richard Cecil, Memoirs of the Rev. John Newton, in The Works of the Rev. John Newton, Vol. 1 [The Banner of Truth Trust, 1985], 108.)

"For I consider that the suffering of this present time are not worth comparing with the glory that is to be revealed to us" (Romans 8:18).