The Chinese script is not an alphabet like in English; instead, it uses characters to represent whole words, often based on their meaning rather than their pronunciation. For example, the character 木 means 'tree' and you can see the way that the meaning is represented in the character. However, most characters are not made of just one part (like 木) - they will usually have 2 parts, but some characters can have up to 11 parts. These parts are called 'radicals' and they are the building blocks for all the bigger characters (in fact, the indexes of Chinese dictionaries are often ordered by radical).
An example of this could be the word 妈, which means 'mother'. The left-hand radical of this character is 女 ('woman') and the right-hand radical is 马 ('horse'). In these types of characters, the left radical shows the general meaning and the right radical shows the pronunciation. In this case, 马 'horse' is pronounced ma3, while 妈 'mother' is pronounced ma1 so the similarity in pronunciation is clear. The importance of the radicals is that they allow you not only to have an idea what is being represented (i.e. 'something female') but also how it is pronounced (i.e. 'similar to ma3').