Styles allow you to combine many different formatting features together. The most common style is the Normal style, which is the default style for documents. You can change the settings of any style. For example, many people change the size of the Normal style from 10 pt. You can also create your own styles, either by modifying an existing style or creating your own from scratch.
Templates are an extension of styles.
A template is a collection of multiple style definitions. If you are writing a Masters' thesis, you may need to follow a particular set of style definitions as outlined by your graduate advisor. You might define your own styles for quotations, for headers and footers, for bibliographic citations, etc. You could save this unique set of style definitions in a template, and apply the template to your Masters' thesis. Then, if you needed to insert a bibliographic citation, you would already have the correct style definition available.