"Behold, I am ready and prepared to fulfil the mitzvah. As is written in the Torah: You shall count from the day after the day of rest, from the day you bring the Omer as an offering."
The Arizal and his followers instituted the practice of adding "Hin'ni Muchan Umzuman" before many different mitzvot. This well-known, traditional melody is used each time, with the text changing to suit the mitzvah. As an example, the version preceding Friday night Kiddush can be found in Israel Goldfarb's "Sabbath in the Home", and a quick peruse online will yield versions for introducing Birkat Hamazon, for each of the four cups on Seder night and many others.
For whatever reason, some of these liturgical additions have found more popularity than others, and none more so than Sefirat Haomer, to the point that for many, this melody seems to now be inextricably linked to the Sefira. This is somewhat ironic, as according to most commentators, the mitzvah of counting the Omer is only considered to be a mitzvah d'orayta while the Temple stands, and some have suggested that saying the words "I am prepared to fulfil the mitzvah as is written in the Torah" over a mitzvah d'rabbanan constitutes a contravention of ba'al tosif.
In any event, this catchy melody has become an established minhag in many communities the world over.