Making your style public will allow anybody to view or use the style. Public styles can be searched by username at [http://www.insanejournal.com/styles/browse/]. If you are cautious about certain users using your styles without permission, please do not make your styles public.
At the Edit Style page, under the box for the name of your style, you will find a heading labeled "Style Options". There will be a checkbox for the "Public?" setting. If you want to make it public, click it. If not, make sure the box is unchecked. Then, save your style.