Many tags do not have a description, but I did not find a button to write/suggest such a description.
When you are the first person to create and use a new tag it's considerate to at least write the excerpt for the tag so no one has to guess what it's used for and the possibility of use for multiple meanings is avoided. Lower reputation users might earn +2 reputation for writing one good sentence, your small contribution is worthwhile for everyone.
It's also kind to write the second half too, please come back when you have time available and find nothing else to do during your visit. Reputation is also awarded for the second edit. Some guidelines are offered in this answer.
For tags that don't have a wiki or excerpt yet:
https://or.stackexchange.com/questions/tagged/<tag-name> and click the "help us create it" link. You can also go to
https://or.stackexchange.com/tags and click on a tag to get to this page.
You can also click the "Learn more..." link, bringing you to the URL
https://or.stackexchange.com/tags/<tag-name>/info and click the "Propose tag info" button.
For questions that already have a tag wiki/excerpt:
Go to the page
https://or.stackexchange.com/questions/tagged/<tag-name> and click "Improve tag info". (I had to take a screenshot from another site since I couldn't find a tag with a wiki here)
You can also go to
https://or.stackexchange.com/tags/<tag-name>/info and click "Edit Tag Info".
From the Stack Overflow Blog:
If you click the see all tag synonyms » link from any specific tag page, you can browse all current and suggested tag synonyms, across all tags. If you’re a moderator, you should have this page bookmarked.
It is our hope that these tag synonym pages are fairly self-explanatory, at least to the higher reputation users that they are designed for. And if not, we’d like to make it so.
If you’d like to help tame the tag folksonomy with us:
browse the info tab for tags you actively participate in
edit the tag wikis to make them better
vote for the tag synonyms you think should (and shouldn’t exist)
suggest new tag synonyms we might need
monitor the master tag synonym page and see which ones are working, and which ones aren’t.
We need your help to make the page 1 and page 2 tags great — so please pitch in and contribute a tag wiki excerpt or edit a tag wiki excerpt to make it better. To invite editing, there’s a small edit link that will dynamically appear as you mouse over the tags page if you have enough reputation.
Here’s a few words of advice on writing tag wiki excerpts:
The excerpt is the elevator pitch for the tag. You only have ~500 plain text characters for the excerpt, so don’t feel obligated to cover everything in it! Save that for the 30,000+ character Markdown tag wiki. The excerpt should define the shared quality of questions containing this tag — boiled down to a few short sentences.
Avoid generically defining the concept behind a tag, unless it is highly specialized. The “email” tag, for example, does not need to explain what email is. I think we can safely assume most internet users know what email is; there’s no value in a boilerplate explanation of email to anyone.
Concentrate on what a tag means to your community. For “email” on Server Fault, mention the server aspects of email including POP3, SMTP, IMAP, and server software. For “email” on Super User, mention desktop email clients and explicitly exclude webmail, as that would be more appropriate for webapps.stackexchange.com.
Provide basic guidance on when to use the tag. In other words, what kinds of questions should have this tag? Tags only exist as ways of organizing questions, so if we don’t provide proper guidance on which questions need this tag, they won’t get tagged at all, rendering the tag excerpt moot. Think of it as a sales pitch: in a room full of tags screaming “pick me!”, what would convince a question asker to select your tag?
Some tags are common knowledge. Most tags require a bit of explanation in the excerpt, even if it’s only 3 or 4 words. But if the tag is common knowledge — that is, if you walked up to any random person on the street and said the tag word to them, and they would know what you were talking about — then don’t bother explaining the tag at all. Stick to usage of the tag within your community in the excerpt.
Even if you have good tag wikis already, it’s healthy for communities to introspect a bit about their use of tags, and what those tags mean. Periodically asking questions like “who would ever subscribe to this tag, and why?” can reveal a lot about the nature of tagging on your site.
If it says "edit pending" in place of "Propose Tag Info", then it means someone has already proposed an edit but it hasn't been reviewed yet. The system won't let you propose more edits until the pending edit is cleared, it seems. Clicking "edit pending" just takes you to a help page about editing tag wiki privileges. I assume that for now the CMs are the ones to approve those edits.