Annotations are typically used as the definition of annotation states:
A note of explanation or comment added to a text or diagram
Annotations can often be used to assist in the explanation of content, or assist users and direct them where they should be looking. For example, often times in YouTube videos you will see annotations used as a method to ask for user participation in the form of "likes, comments, and favourites". Annotations in YouTube videos are also usually used to link a user to another related video on the topic of discussion.
An annotation can increase usability and make things easier to follow, thus positively enhancing a user's experience. On the other hand, overusing annotations can also cause user related issues. Using YouTube as an example again; if a video is cluttered with useless annotations all over the page that serve no real purpose they can be annoying at certain points.
Some other common examples of annotation usage is in images. For example someone could be showing you a large picture, but they only want you to look at one specific region of this image. In person they normally could just point it out to you, but digitally an alternative is to use some kind of arrow, or circle to highlight the region of interest. Typically these would be classed as annotations.