The weather in Israel at this time is often characterized by hot winds. In Hebrew the more "proper" name is sharav שרב - but the popular name is the Arabic hamsin (or khamsin). The name hamsin has nothing to do with the Hebrew word cham חם - hot.
The word hamsin in Arabic actually means fifty. This derives from an Arabic tradition that there are 50 days of these hot winds. Judaism has a similar tradition. To understand this, it's important to note that despite Hebrew words for the four seasons known in English, the climate in the Land of Israel really only includes two seasons - summer and winter. Between each season there is a transitional period that is a very sensitive time for agriculture. Untimely heat, rain or winds can cause great damage to the crops. As part of the prayer for a successful transition, both periods include mitzvot that involve waving in all the directions of the wind. The Rabbis explain both the waving of the lulav and the omer as connected to a prayer that the winds be favorable.
The transition from winter to summer is longer than the one six months later, and therefore is more sensitive. Prof Jacob Milgrom notes:
that counting betrays anxiety. The spring harvest coincides with the end of the rainy season but also with the onset of a period when Israel is often buffeted by the hot, dry east wind called Sirocco, blowing across Egypt. The contemporary Israeli name for this feared phenomenon is Hamsin, which derives from the Arabic word hamsun and is related to the Hebrew cognate hamishim, all meaning 50. The Mishna preserves the ancient angst: "At Passover the world is judged in terms of the grain harvest." Hence, from April to June (roughly a 50-day period), the earth's bounty stands in jeopardy of being depleted by the withering winds of a Hamsin.
Each day counted therefore constitutes both thanks to God that the previous days passed without damage to the crops, and a prayer that the remaining days will be successful.