Filegroups are named collections of files and are used to 
help with data placement and administrative tasks such as 
backup and restore operations.

Filegroups are group or collection of Files that is used to 
maintauined the transaction of Data and Restore Operations.

Filegroup is a logical container for the collection of 
datafiles.(.mdf or .ndf that is primary file group or 
secondary file group)
Every database contain 2 file groups
1.Primary file group, which Contains all the primary data 
files any other Secondary  datafile which is not 
specifically allocated to anyother file groups
2.User defined file group:It is created by the user to 
group the datafiles

3.transaction log file:Does not belong to any file group.A 
database can have maximaum of 32,767 file groups

Example:
Create database student
on Primary ***Primary
(
name='student_pri_data1.mdf',
filename='g:\student_primary_data1.mdf',(Location of this 
file group)
size=2mb
maxsize=10mb
filegrowth=1mb
),
filegroup student_group1 ***Secondary
(
name='student_Sec_data1.mdf',
filename='g:\student_sec_data1.mdf',(Location of this file 
group)
size=10mb
maxsize=12mb
filegrowth=2mb
)
log on  ***log file
(
name='student_log_data1.mdf',
filename='g:\student_sec_data1.mdf',(Location of this file 
group)
size=12mb
maxsize=10mb
filegrowth=1mb
)