Our Scripture reading today is Luke 14:31-33.
Verse 33, "So likewise, whosoever he be of you that forsaketh not all that he hath, he cannot be my disciple." 
The idea of forsaking all of our possessions is a willingness to say goodbye to them or part ways with them.  It is not the having of things that is the problem.  There is a big problem, however,  when things have us.  If our decision making process is affected by trying to keep what we have or even have more, we are in danger of not being His disciple.  
What we are challenged with in these verses is a decision to live for eternity.  The possessions we have on this earth can be used for eternal value.  It is our responsibility not just to collect a bunch of "toys", but to use the things God has given us to serve Him and point others to Him.  Since all that we have is from the Lord, there should be a yielding of everything back to God.