You need a post box to get mails in Dubai. UAE has many post offices and you will be alloted a post box in your nearest post office. You need to submit your
- Passport copy with residency stamp
- Two passport size photographs (It must be valid for at least 6 months)
- A completed form you will find from the post office.
Or you can also apply online : https://www.epg.ae/postbox/
You can find more details here : http://gulfstay.com/blog/po-box-rental-dubai