How does NASA get a 360 degrees texture map of Earth?
If you're asking about how they are able to distinguish different layers of information on the Earth, your answer is found in the field of Remote Sensing. Using sensors running on several satellite systems (e.g. MODIS, ETM) that are isolated to pick up specific radiative bands (IR, NIR, Visible, etc.) you can derive some pretty amazing information.

Using map algebra on these bands, you can figure things out like cloud cover, vegetation health, elevation, temperature and land cover of the surface, etc. Many of these data sets can be found directly through NASA or USGS. Creating masks of different information using these techniques can lead to really amazing visualizations.

The really fascinating thing is that a lot of this information can be calculated on the fly using raw data and any GIS infrastructure or scripts. That's likely how NASA is able to visualize these data products the moment they collect them.