Hi Friend
Plz go through these 3 points , carefully absorb and it
might be clarified your doubts.

1)Need of function modules is to avoid the lengthy  and
faster accessing data,how means,suppose for example: i want
the previous month first day and last day based on Today
date(means day Sunday or Monday or etc)Actually today date
is 19Apr2008,Saturday. I want previous month first day and
last day, ie first day is 1Mar 2008 it is Sunday or Monday
or Tuesday etc and  like last date 31Mar 2008 is Monday or
Tuesday etc. Generally you need to write lengthy coding , so
to avoid lengthy coding just u use date function module in
coding and pass the parameters, it will give the out put to
u(just few lines of coding)

2)Function groups means, some related function modules are
grouped in to one function group.
For Example: For date lot of different date function modules
are available in SAP R/3, so these function modules are
grouped in to one Function group.

3)Subroutines are used in only with in the program.
Frequently used part of program is keep in to subroutines. 
Globally not available. But where as Function modules are
available in central library of R/3 and global access.

If any doubts plz contact me via mail : malli.gontla@gmail.com