Confusing the Saten
Many special practices are observed in connection with Rosh Hashana for which the explanation given is "to confuse the Satan." For example, the fact that Rosh Hashana also marks the beginning of a new month is never mentioned in our prayers; the upcoming month of Tishrei is conspicuously not blessed on the Shabbat preceding the New Year; and the shofar is not sounded in the synagogue on the day before Rosh Hashana. In fact, one of the reasons cited for blowing the shofar during Elul (except for the last day of the month) is to confuse the Satan "so that he does not know when Rosh Hashana will be."
What is meant by "confusing the Satan"? Who is this Satan anyway, that he can be confused by such transparent means, repeated from year to year?
The Satan is an accusing angel whose function is to bear witness against the Jewish people. When Jews obey G-d's command by sounding the shofar on Rosh Hashana, they thereby demonstrate their love for the Torah and its mitzvot (commandments). Rather than literally "confusing" the Satan, the prosecuting angel's arguments are stopped in their tracks in the face of such devotion. Observing the mitzva of shofar weakens the Satan's grounds for criticism and deflates his case before G-d in the Heavenly Court.
The other things we do "to confuse the Satan" may also be explained in this light. Blowing the shofar throughout the month of Elul brings the Jewish people to true repentance even before Rosh Hashana, nullifying the Satan's arguments before he is called to testify. Not sounding the shofar on the day before the New Year proclaims to the entire world that the Jewish people have already done teshuva and have no further need to hear it! When the Satan sees how confident the Jews are that they will emerge victorious in judgement his voice is stilled.
Similarly, not drawing attention to the fact that Rosh Hashana marks the beginning of a new month may be explained with the following analogy: When engaged in battle, military strategy dictates that an army not reveal all of its weaponry to the enemy, lest the opposing side intensify its campaign against them. We do not mention the new month (and the many merits accrued by the Jewish people in its observance) so as not to arouse the Satan to boost his efforts and devise new strategies.
Just being cognizant of the lengths one must go to in order to "confuse the Satan" in itself brings a Jew to teshuva, ensuring a favorable judgement and a good and sweet year for the entire Jewish people.
Adapted from the works of the Lubavitcher Rebbe