About both. The purpose of a tag wiki excerpt is to guide people when they are deciding how to tag a question.
If the meaning of the tag is not generally known to anyone who would ask a question in that field, then the excerpt should explain it. For example, algorithms does not need a definition, but reductions does. The excerpt doesn't need to have a correct and complete definition, it's enough to give the context.
The excerpt should concentrate on the usage of the tag on the site. If the word has other meanings that are not applicable to computer science, this is irrelevant (unless there is a popular misconception to dispel). If the way the tag name is interpreted on the site is not the way every reasonable computer scientist would understand it, then the excerpt should contain enough guidance to understand what the tag means here.
If there is a risk of confusion between several tags, or if there are many off-topic questions in the tag, then the excerpt may need to mention what questions should not have this tag, and possibly where to ask the question instead. This is fairly rare; related tags and sites are usually only mentioned in the tag wiki.
The official guidance on tag wiki excerpts is in the blog post Improved tagging. For tag wikis in general, read Redesigned tags page.