Have you read this section of the help? You really need a handle on these concepts to work with raster data effectively -- so if you haven't read this overview yet I highly recommend it to you:
ArcGIS 10.0 help: What is Raster Data?
You seem to have a start as the extents are the extent of the dataset, which includes all cells, those with data and cells that are NoData.
Count is the number of data cells found in that zone, Area is the total area (count times the square of the cell size used in the calculation), and Sum is the sum of the values data cells in the zone. The online help for Zonal Statistics as Table has an example that shows this pretty clearly.
You may be wrong about the cell size though -- you said the raster dataset has a cell size of 1m but your screen shot shows a cell size of 0.87.
Hope this helps.
In the above screenshot I made a mistake and said my Cell Size was 1...that was for another raster. But in the above shot, what would the total area of the raster be? 333,638 meters? data is in UTM.
>>> 333 * 638 * (0.87999999 ** 2) 164524.37759962608
The total area of the raster is the total area of all the cells in the raster's extent: rows x columns x (cell size)2. (All rasters are rectangular.)
In the case of your screen shot, using my handy Python calculator:>>> 333 * 638 * (0.87999999 ** 2) 164524.37759962608
The area of data cells is a different question; that number is in your zonal statistics output for each zone in the "zone raster" you provided to the tool.