If you take a look at the docs for the select() command, you will see that it reports it has no return value :
http://help.autodesk.com/cloudhelp/2016/ENU/Maya-Tech-Docs/CommandsPython/select.html
The following code is getting a None return value from the select() call:
result = cmds.select( cmds.listRelatives(cmds.ls(selection=True), children=True))
You are passing the results of listRelatives() to select(), which is what you wanted, but if you also want to print that return value then you want to capture it to a variable first:
result = cmds.listRelatives(cmds.ls(selection=True), children=True)
print result
cmds.select(result)
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