In the KJV the word apotassó which is used in Luke 14:33 is translated as "forsake" and in the NIV that same word is translated as "give up". For some this means that all Christians are supposed to sell everything they have and generally give the proceeds of their sale to their church or ... the leader of the group. Curious as to why the Mounce Reverse-Interlinear New Testament translated apotassó as "renounce", I decided to do a bit of research.
The definition of apotassó is: I withdraw from, take leave of, renounce, send away. The definition of renounce is: to refuse to follow, obey, or recognize any further.
In other words, Jesus is telling us that we are no longer to be under the authority of our possessions, we are to be under the authority of God. Now, you may be thinking to yourself that no one is under the authority of their possessions. Really? Nowadays, in the US, your credit card company is required to disclose exactly how long it will take you to pay off your debt to them if you only make minimum payments each month. For most Americans, that number is twenty to thirty years... per credit card. If this is you, than you are under the authority of your possessions. No? Well, exactly what did you use that credit card for? Emergencies? Been there done that. It's time to get honest about this and quit making excuses. You may have used it for an emergency but that was because you didn't have enough money to cover the emergency because... you bought something because you wanted it, not necessarily because you needed it.
If you say, "I would love to give but I can't because I have too many bills to pay (including credit cards and loans to buy stuff)", you are under the authority of your possessions. On the other hand, if you say "I don't want to give because what's mine is mine!" you are under the authority of your possessions as well. If you don't have "time" to serve God or be with your family because you need to work an extra job to either pay for "stuff" or accumulate more "stuff, you are under the authority of your possessions. I think you get the idea. Whose authority are you under?
So how do you get out from under the authority of your possessions or anything else other than God? You renounce it and declare that you are no longer going to follow it, you are going to follow God. Does this mean, for example, that God is going to suddenly pay all your bills in full and you go merrily on your way doing the same old same old? Probably not, but if you listen to Him and follow His directions in this matter, you will eventually make that last payment and you will be amazed at how quickly that happens when we renounce the authority of the things of this world and follow Jesus Christ.