What does the dns-search option mean in /etc/network/interfaces?

dns-search determines which domain is appended for dns lookups.

Normally you will specify here the same domain as returned by hostname -f.

For detailed information see the following quote from man resolv.conf:

search Search list for host-name lookup.
    The  search  list  is  normally  determined from the local domain name; by
    default, it contains only the local domain name.  This may be changed by listing
    the desired domain search path following the search keyword with spaces or tabs
    separating  the  names.  Resolver queries having fewer than ndots dots (default
    is 1) in them will be attempted using each component of the search path in turn
    until a match is found.  For environments with multiple  subdomains  please read
    options ndots:n below to avoid man-in-the-middle attacks and unnecessary traffic
    for the root-dns-servers.  Note that this process may be slow and will generate
    a lot of network traffic if the servers for the  listed  domains  are not local,
    and that queries will time out if no server is available for one of the domains.

    The search list is currently limited to six domains with a total of 256 characters.