the find command returns a list of files, and the -exec parameter executes on each listed file the command chmod 644. The brackets allows the user to specify where in the command is used the listed filename...
the \; is used to specified the end of the command (in this case, the end of the chmod command)
see man find:
-exec command ;
Execute command; true if 0 status is returned. All following
arguments to find are taken to be arguments to the command until
an argument consisting of ';' is encountered. The string '{}'
is replaced by the current file name being processed everywhere
it occurs in the arguments to the command, not just in arguments
where it is alone, as in some versions of find. Both of these
constructions might need to be escaped (with a '\') or quoted to
protect them from expansion by the shell. See the EXAMPLES sec-
tion for examples of the use of the '-exec' option. The speci-
fied command is run once for each matched file. The command is
executed in the starting directory. There are unavoidable
security problems surrounding use of the -exec option; you
should use the -execdir option instead.
http://unixhelp.ed.ac.uk/CGI/man-cgi?find