I don't think Christ meant that every believer should give up all of their material possessions, but I think Matthew Henry puts it in the context for which Christ meant it; namely:
"They(Followers of Christ) must be willing to quit that which was very dear, and therefore must come to him thoroughly weaned from all their creature-comforts, and dead to them, so as cheerfully to part with them rather than quit their interest in Christ."
Meaning by possession all those things which formerly were very dear to us, but when Christ is revealed to us we must embrace Him with no reservations and if the continuity of that relationship means becoming a pauper, then so be it, for we have gained treasure in heaven by doing so.
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