Warning: The disk usage for one or more of your partitions is running low

How many times this week I received a warning email messages
I connected to admin user and I saw on the "Complete Usage Statistics" the following lines


Filesystem        Size        Used        Avail        Use%        Mounted on
/dev/mapper/vg_*-lv_home        337G        65G        255G        21%        /home
/dev/mapper/vg_*-lv_root        50G        45G        2.7G        95%        /
/dev/sda1        485M        36M        424M        8%        /boot

Is it critical?
How do I fix this?