The resolution of the data is mostly 3 arc seconds (90 m), but for some regions you can download data with a resolution of 1 arc second (30 m). These regions are colored red in this tool.
The first source is NASA. This source provides (recalculated versions of) the original data.
These data have some drawbacks: there is no data north of 60° N or south of 60° S, and there are voids in the data for some mountain and desert areas.
(Apparently you need to have an account for this...)
The second source is Viewfinder Panoramas of Jonathan de Ferranti. He has done a great job to extend the coverage to the whole earth and to correct the voids in the original SRTM data.
This source is the preferred one; that's why this one is selected by default.
How does it work?
First decide which tiles you need. If you got to this page when using JaVaWa RTWtool, the needed tiles are already selected for you.
Don't try to download every tile on the map; it's a huge amount of data, and will put too much stress on the servers that provide the data.
Next, choose which source you want to download the tiles from.
Select the tiles by clicking on them (for the NASA data, you need to zoom in until the grey tiles turn blue or red); the links to the tiles will appear in the list on the left. The resolution of the selected tiles is indicated in the list.
You will have to download the tiles (or sets of tiles in the case of Viewfinder Panoramas) manually one by one by clicking the links in the list. Put the downloaded files in a folder and select this folder in JaVaWa RTWtool.