If you are seeing errors about the disk being not being sufficient, there are things you can do to debug and fix that.
First, let's confirm that you indeed are out of disk space. Via SSH connection (the terminal) issue the following command (df -h):
1[otsmanager@host ~]# df -h
2Filesystem Size Used Avail Use% Mounted on
3tmpfs 383M 892K 382M 1% /run
4/dev/sda1 38G 4.4G 32G 13% /
5tmpfs 1.9G 0 1.9G 0% /dev/shm
6tmpfs 5.0M 0 5.0M 0% /run/lock
7/dev/sda15 253M 6.1M 246M 3% /boot/efi
8tmpfs 32M 44K 32M 1% /var/lib/php/sessions
9tmpfs 382M 8.0K 382M 1% /run/user/1000
You can see in the output that it shows the percentage of disk space used for every "partition" mounted. The last two columns are most useful: the percentage of space used and the mount point. You are primarily concerned with the first line where the mount point is /. If it is at 100%, you are out of disk space.
It is also possible that you are out of inodes. This situation will make you unable to create new files even though you still have disk space left. An inode is, simply speaking, a file or a directory. Therefore, there is certain maximum limit of files and directories you may have, usually it is high enough for any normal usage.
To confirm if you are running out of inodes, run df -i:
1[otsmanager@host ~]# df -i
2Filesystem Inodes IUsed IFree IUse% Mounted on
3tmpfs 488964 758 488206 1% /run
4/dev/sda1 2427136 138875 2288261 6% /
5tmpfs 488964 1 488963 1% /dev/shm
6tmpfs 488964 4 488960 1% /run/lock
7/dev/sda15 0 0 0 - /boot/efi
8tmpfs 488964 14 488950 1% /var/lib/php/sessions
9tmpfs 97792 29 97763 1% /run/user/1000
As you can see, the IUse% is low, it's usage is just 21%. However, certain cases - such as a lot of PHP session stored on the disk, could possibly exhaust this limit.
Excessive logs
What typically happens is that your log files are taking too much space. This typically doesn't happen because the system (and journald) are configured to only occupy certain disk space %. However, you can simply check how much space your logs are taking using du -hs /var/log:
1[otsmanager@host ~]# sudo du -hs /var/log
239M /var/log
In this case logs take only 39 MB. If you find that they take too much, you can further look what subdirectory takes most disk space:
1[otsmanager@host ~]# sudo du -hs /var/log/*
216K /var/log/alternatives.log
3152K /var/log/apt
44.0K /var/log/aptitude
51.9M /var/log/auth.log
63.1M /var/log/btmp
7104K /var/log/cloud-init.log
888K /var/log/cloud-init-output.log
98.0K /var/log/dbconfig-common
104.0K /var/log/dist-upgrade
11312K /var/log/dpkg.log
124.0K /var/log/fsck
1333M /var/log/journal
144.0K /var/log/kern.log
1512K /var/log/lastlog
168.0K /var/log/mysql
17112K /var/log/nginx
184.0K /var/log/php7.0-fpm.log
198.0K /var/log/syslog
20416K /var/log/syslog.1
218.0K /var/log/unattended-upgrades
228.0K /var/log/wtmp
We see that /var/log/journal is taking most disk space. Although it is not recommended, you can remove your logs if you are out of disk space:
[otsmanager@host ~]# sudo rm -rf /var/log/journal/*
Watch out how you are typing the above command, you can potentially remove something important if you misspell it!