The custom of Tashlich has its basis in a Medrash (Tanchuma Vayeira 25):
"When our forefather Abraham went to bind his son Isaac (in preparation for
his offering of his son), Satan led him through a river until the water
came up to his neck. Abraham said ' Help, Hashem, for water threatens our
lives!' Then, he (Abraham) was saved."
Abraham was given a test - a command to sacrifice his only son, Yitzchok.
The Satan did all that he could to prevent Abraham from passing the test.
He placed obstacles in front of Abraham so that perhaps Abraham would find
an excuse not to perform the act of ultimate sacrifice. One of these
obstacles was an impassable river. Abraham was not deterred by the fact
that there was a formidable challenge in the form of a river in front of
him. He walked into the water, and did all that he could: He prayed to G-d
for assistance. The assistance came. The river vanished. Abraham was able
to continue on his travel and he ultimately passed this most difficult test.
Our prayers at a body of water on Rosh HaShana are meant to recall this
incident. We remind Hashem of the great determination of our forefather,
how great his desire was to fulfill His word, to perform this act of
sacrifice. We are the children of Abraham, who save some kernel of the
devotion and will of our grandfather within us. We also remind ourselves
on the day on which we are written for a good year of how we are to
dedicate ourselves to Hashem. We are to remind ourselves when we look at
the body of water that no matter how great an obstacle seems, when it comes
to the service of G-d, we can overcome it. If the situation is so difficult
we fear that we can not handle it, we can do what Abraham did: pray.
This year, because the first day of Rosh HaShana is on Shabbos, many have
the custom to perform Tashlich on the second day of Rosh HaShana. No matter
what day we perform Tashlich, may it serve to inspire us, to increase our
devotion and dedication to G-d for the upcoming year, and may the merit of
Abraham's devotion assist us as well in this critical time of judgment.