Basically, this effects the icon and where the posting is located in the forum topic listings.
Sticky and Announcements will always be located at the top of the forum listing above all the "normal" postings. This is so people can see/find them easily.
In general, Announcements are stuff that forum admins or moderators will be posting (like FAQ or Forum Rules).
Sticky's are more generally stuff that starts out as a normal thread but then because they contain good information or a common topic are "sticky-ed" to the top. (e.g. How to get X to work with Vista? sort of thing) [originally posted on jforum.net by monroe]