A radical is the part of a Chinese character that often gives a clue to the character's meaning. For example, the word 湖 hu2, meaning lake, is built from another character 胡 pronounced hu2 that means beard , but it has a water radical 氵 on the left, meaning that the character sounds like hu2 but has a water-related meaning.
Radicals don't always convey meaning, sometimes they just differentiate a sound. For example, if you add the jade radical to 里 li3, which means mile, you get the word 理 "principle".
Radicals are used to help categorize characters for dictionaries. Characters will be grouped under the same radical, which narrows down the search. Experts differ on the exact number of radicals in Chinese, but 214 is a commonly used number.
You have to have some understanding of Chinese characters to find the radical and look up the word in a dictionary. Radicals may be written differently depending on where they are placed in the character. You also just have to know what to look for.