A staging area, or landing zone, is an intermediate storage area used for data processing during the extract, transform and load (ETL) process. The data staging area sits between the data source(s) and the data target(s), which are often data warehouses, data marts, or other data repositories.
Above is the standard defination of Staging Data in Wikipedia. So, staging data is a set of DataBases and tables where raw data will be stored.
Example, assume that you are working for a digital marketing company. They will tie up with various vendors to do digital marketing like, Facebook, Google and many more. Different vendors will provide marketing campaign data into different format, like one vendor will give data in form of CSV via FTP, another may expose API, other may give raw XMLs. So, you gather all data and first store it into one database. That is called staging data.
Dimension is the way you want the data to be fetched. Example, in marketing campaing, you may need report country wise, weekly, montly. So, your input to get reprot is your dimention.
Facts are actual data. Example in marketing campaing last week you had 2k views. So, last week is your dimension and 2k views is your fact.