How to Download
Click on the "Data" link towards the top of the page. Then you will be presented with a picture of the countries. Click on the country of interest, then scroll to the bottom. There is a quick form you will need to complete to download the file. You can unzip the files using the open source program 7-zip. Each zipped country file comes with several different Geotiffs--two for each estimated year (2010 and 2015) as well as 'adjusted' and 'unadjusted' estimates based on UN data.
"High resolution, contemporary data on human population distributions are a prerequisite for the accurate measurement of the impacts of population growth, for monitoring changes and for planning interventions. The AsiaPop project was initiated in July 2011 with an aim of producing detailed and freely-available population distribution maps for the whole of Asia."