Normally an inode is used for each files on the filesystem. Its contains,

File permission
File Owner ID
File Group ID
Size of file
Number of hard links to the file
Time last accessed 
Time last modified file
Time inode last modified

If you have received an output running out of inodes, basically you have got lots of small files in your system, So you need to find and remove unwanted files from the system.

For example: To findout Inode usage, you can see the Iuse% is 100% of the file system /dev/sda1

# df -i

Filesystem            Inodes   IUsed   IFree IUse% Mounted on
/dev/sda1            2565120 2565120       0  100% /

# find / -xdev -printf '%h\n' | sort | uniq -c | sort -k 1 -n

1112 /usr/share/man/
2514 /usr/share/man/
809588 /var/spool/postfix/maildrop

Note : Before remove make sure that directory 

Now, You need to remove files from the maildrop directory. Some times you can not remove the files from that maildrop directory, so give the below command to find and remove.
# find /var/spool/postfix/maildrop/ -name  '*'  -type d | xargs rm  -rf