The way to think of this is that ## gets replaced by # in just the
same way that #1 gets replaced by 'whatever is the first argument'.
So if you define a macro and use it as:
\def\a#1{+++#1+++#1+++#1+++} \a{b}
the macro expansion produces '+++b+++b+++b+++',
which people find normal. However, if we now replace part of the macro:
\def\a#1{+++#1+++\def\x #1{xxx#1}}
\a{b} will expand to '+++b+++\def\x b{xxxb}'. This
defines \x to be a macro delimited by b, and taking no
arguments, which people may find strange, even though it is just a
specialisation of the example above. If you want \a to
define \x to be a macro with one argument, you need to write:
\def\a#1{+++#1+++\def\x ##1{xxx##1}}
and \a{b} will expand to
'+++b+++\def\x #1{xxx#1}', because #1 gets replaced by 'b'
and ## gets replaced by #.
To nest a definition inside a definition inside a definition then
you need ####1, as at each stage ## is replaced by
#. At the next level you need 8 #s each time, and so on.