You need to edit the category file, switch the the_content bit of code with the_excerpt bit where it says something like, while have posts. Blah blah, the_post and so on. of course you need to have excerpts in your posts. Otherwise if you want text snippets of your posts you need to add parameters to output the_content truncating it after a custom number of letter ending with an ellypses or similar and a link to the post with read more or some. The codex has lots of references on this, and the forums are filled with such cases, search around.