The category is a broad label assigned to each agenda item. By default, the category is simply derived from the file name, but you can also specify it with a special line in the buffer, like this1:
#+CATEGORY: Thesis
If you would like to
have a special CATEGORY for a single entry or a (sub)tree, give
the entry a :CATEGORY: property with the special
category you want to apply as the value.
The display in the agenda buffer looks best if the category is not longer than 10 characters.
You can set up icons for category by
customizing the org-agenda-category-icon-alist
variable.
[1] For backward compatibility, the following also works: if there are several such lines in a file, each specifies the category for the text below it. The first category also applies to any text before the first CATEGORY line. However, using this method is strongly deprecated as it is incompatible with the outline structure of the document. The correct method for setting multiple categories in a buffer is using a property.