Running check for fragmentation on /home says there are errors. What does it mean?

I ran the fragmentation check “sudo /sbin/fsck -nvf /dev/sda3” on my /home drive and got:

fsck from util-linux-ng 2.17.2
e2fsck 1.41.11 (14-Mar-2010)
Warning!  /dev/sda3 is mounted.
Warning: skipping journal recovery because doing a read-only filesystem check.
Pass 1: Checking inodes, blocks, and sizes
Pass 2: Checking directory structure
Pass 3: Checking directory connectivity
Pass 4: Checking reference counts
Pass 5: Checking group summary information
Free blocks count wrong (48018785, counted=48007817).
Fix? no

Free inodes count wrong (17951025, counted=17949381).
Fix? no

/dev/sda3: ********** WARNING: Filesystem still has errors **********
                                                                                                                                                                                 
  145103 inodes used (0.80%)                                                                                                                                                     
     639 non-contiguous files (0.4%)                                                                                                                                             
      55 non-contiguous directories (0.0%)                                                                                                                                       
         # of inodes with ind/dind/tind blocks: 0/0/0                                                                                                                            
         Extent depth histogram: 144410/167                                                                                                                                      
24354719 blocks used (33.65%)                                                                                                                                                    
       0 bad blocks                                                                                                                                                              
       6 large files                                                                                                                                                             
                                                                                                                                                                                 
  120985 regular files
   23592 directories
       0 character device files
       0 block device files
       0 fifos
     214 links
    2160 symbolic links (2159 fast symbolic links)
       1 socket
--------
  146952 files

What does this mean? Are these serious errors? How should I fix this?

Hard to say since the filesystem is still mounted. Have you tried unmounting it and re-running the fsck command?

No. How would I do that since I’m running a user that is in /home?

There are a few different ways. You could login to the machine as the ‘root’ user, then umount /home. It’s easier to do this if you logout of KDE/GNOME/XWindows (assuming you are logged in that way), then either re-logging in as the ‘root’ user, or hitting CTL-ALT-F1 and logging in as ‘root’ from the console.

You could also boot into single user mode, unmount /home, and re-run your fsck command.