This is just my guess but there might be better answers if one digs around the net. 漢 was a kingdom that existed more than 2000 years ago. And perhaps that's the root or origin of the chinese medicine we see today. 方　has the meaning of way, or direction as well. So I'm guessing it's trying to point out that the medicine comes from the 漢 era. I'm sure there might be better answers, but this is my take on it.

I'm not familiar with Japanese (I only started learning it very recently), but I think I can make a pretty good guess based on my knowledge of Chinese Hanzi (from which Japanese Kanji is derived from). "漢/汉" refers to the Han race, the ethnic group that makes up the vast majority of Chinese people. It's the same character that's used in "漢語/汉语" (Chinese language) and "漢字/汉字" (Chinese characters). "方" means 'side'. I'm guessing it's used to mean "Chinese side" in the same way "西方" refers to the West. For what it's worth, I looked up "汉方" in my Chinese dictionary and it just says "Kampo {ie. the Japanese form of Chinese medicine}, so it looks like the two characters were combined in Japan after Hanzi and Kanji became two separate things.