Its more or less a satirical approach to Japan's society as it exists today.
Notice a prominent similarity to Battle Royale (not plotwise, but in the theme?). The youth of Japan feels neglected, outcast, their parents or their country don't give two shits about them. Noriko's Dinner Table explains some finer points a bit better (if you haven't seen that yet, make sure to do it now AFTER watching Suicide Club) but the overall message is this - if all the Japanese youth were non-existent tomorrow through some/any sort of bizarre happening, would it matter? They are there for themselves and for each other - connected through electronic or internet means - but nobody else notices them around.
Basically that is also the explanation for the "connecting to yourself" part. Do you, as a youth, value yourself as much as you value everything else around you? Because no one else cares or values you (not even the parents, according to the teens). These films basically provide that vision of Japanese society, as seen from an angsty alienated teenager's point of view. The youth feels detached from the mainstream Japanese culture, and they wonder if anyone including their own parents will ever understand them.
Also the symbolism of sudden waves of teenage fashion which come and go - a particular hair style, funkadelic clothes, cells and mobile text msgs etc. Suicide is shown as a grotesque message of the next wave of fashion - with teens jumping on the bandwagon because of the above-mentioned reasons. Their value of life is very little - what matters more to them is to be accepted.
Read this -
http://www.snowbloodapple.com/suicidecircle.htm