tcpwrapped" refers to
tcpwrapper, a host-based network access control program on Unix and Linux. When Nmap labels something
tcpwrapped, it means that the behavior of the port is consistent with one that is protected by tcpwrapper. Specifically, it means that a full TCP handshake was completed, but the remote host closed the connection without receiving any data.
It is important to note that tcpwrapper protects programs, not ports. This means that a valid (not false-positive)
tcpwrapped response indicates a real network service is available, but you are not on the list of hosts allowed to talk with it. When such a large number of ports are shown as
tcpwrapped, it is unlikely that they represent real services, so the behavior probably means something else.
What you are probably seeing is a network security device like a firewall or IPS. Many of these are configured to respond to TCP portscans, even for IP addresses which are not assigned to them. This behavior can slow down a port scan and cloud the results with false positives.
EDIT: Since this post was flagged as plagiarism and deleted, I would like to point out that the assumed source (this page on SecWiki.org) was also written my me. This Security.StackExchange answer (October 31, 2013) predates that page (November 12, 2013) by nearly two weeks. I saw that this answer was receiving upvotes, and as a core Nmap developer I decided that the text would serve as a good addition to our Frequently Asked Questions documentation. It is entirely within my rights, not only as the content creator, but under the Creative Commons Share Alike license stipulated in the StackExchange Terms of Service to redistribute this content in this manner. I recognize that I should have attributed that other content properly, but that is not a reason to remove this post.