It depends on the level (junior/mid/senior) and the company. Obviously, the more you know the more desired you are. Typical daily tasks for me would consist of:
-Disk management. Knowing different RAID levels and what suits your needs best. Knowledge of du, df, mount, fdisk, etc..
-Server load. Why is the load increasing? Is it because all CPU's are being pegged, too much I/O wait time, or what?
-Understanding of syslog, where the logs are stored, and which logs to look at
-Be fluent in a scripting language. Automation is key and good administrators are very lazy and never want to do manual repetitive work
-Be comfortable in kernel compiles and module installs
-Package management. Knowledge of keeping the packages up to date.
-Services. Know all the services that are running on your system. If you don't need them, don't use them as they consume cpu time and memory.
That's just to name a few. As I write this, I realize it's impossible to name everything. Not only do you need to make sure your system behaves properly and efficiently, but also the applications that are installed on them. Popular software that many companies expect you to be very familiar with would be Apache, Samba, Bind, FTP (vsftpd or whatever), Mail (postfix/sendmail/qmail/whatever), and NFS for starters. Then it helps if you know how to setup monitoring tools to monitor the health of your servers/services. This may include graph trending such as setting up MRTG or Cacti+RRD. This helps in troubleshooting and/or prevention of failures down the road. Security is also a big thing. Understand how to harden your system and follow best practices. If your server gets compromised, it is your responsibility.
I wrote this pretty quick and I hope you somewhat get an idea of this role. This is based on my experience.