Does the beta like character (as in 陳, 附 and many more) in Chinese have a special meaning? It probably doesn't. I tried searching but couldn't find one. 
But would be great if it does! Would help me remember so many new words. I hope somebody has figured out a pedagogical role of that symbol.
This radical is called the 双耳旁 or 双二刀, due to it looking somewhat like an ear or the 刀 character. There are actually two radicals depending on whether it's placed to the left or right: 左耳刀 if on the left, 右耳刀 if on the right. The two radicals have different origins and different meanings.

http://baike.baidu.com/view/457766.htm

The left version is derived from the 阜 (fù) character, meaning "mound" or "abundant". Characters with this radical are often related to mountains, hills etc, such as 陵 (hill), 险 (steep), 陆 (terrestrial).

The right version is derived from the 邑 (yì) character, meaning "city". Characters with this radical are often related to cities or human settlements, such as 都 (capital), 郊 (suburb), 郡 (commandery).