writing a brief description of yourself
I would recommend asking whoever is asking you to do this for a past example. Different institutions have vastly different styles -- e.g. some places might be OK with including some humor or random facts in your bio, whereas other places are all business.

That said, you can always get some generic examples by googling "bio examples".

(Also, since this is a workplace question, it's probably more appropriate for https://workplace.stackexchange.com.)