if [ -s "$destdir/$errlogfilename" -a "$sysadmin" != "" ]; then

(-s, condition unknown to me, use "-f" (file) or "-w" (writable)), so
if (something concerning) "$destdir/$errlogfilename" and (-o is or) value for $sysadmin not-is empty(""); then ...

a verbose way to write this would be:
if [ -s "$destdir/$errlogfilename" ]&&[ "$sysadmin" != "" ]; then
or even worse:
if [ -s "$destdir/$errlogfilename" ]; then if [ "$sysadmin" != "" ]; then

An example of "" would be` echo "\"$(true)\" \"$?\""`
You'll see "true" doesn't have output in the std channel (so "" shows only our escaped quotes), only stderr, which, in the case of true always shows "0" for OK.

-s returns true if the file exists and is of length > zero
-a returns true if file exists

The double quotes around the variables exists just in case the
variables contain a space (ie. a filename like '/home/ben/my docs'). If
the quotes are not used the script is expanded such:
and /home/ben/my and docs are expanded by bash as two parameters,
not one. Putting quotes around the variable would expand it to
"/home/ben/my docs".

More good stuff:
http://www.gnu.org/manual/bash/html_...f_6.html#SEC75

-a is mearly a logical and operator...

if [ -s "$destdir/$errlogfilename" -a "$sysadmin" != "" ]

equates to...if "$destdir/$errlogfilename" exists and is > 0 AND "$sysadmin" is not equal to ""

In the script i'm working on....the variable $sysadmin is an e-mail address....root@backup.blahblah

I just didn't see the meaning in "$sysadmin" != ""