From Latin radix (root), in Chinese script, a radical is a root character, i.e., one of 214 basic characters from which all other Chinese characters are derived.
For example, to find a Chinese character in Mathews' Chinese-English Dictionary (and probably other Chinese dictionaries), you first need to identify its radical, then find the character in the radical index, which will give you the character number (these numbers are specific to the dictionary. Then you can find the character inside the dictionary and read both its pronunciation and definition.
This is sometimes very easy, at other times very frustrating, especially when the character seems to be derived from more than one radical or when the shape of the radical is changed within the character (this is often the case because each character is drawn in the same size as any other character, hence the radical is often drawn "compressed").