A unit operation is considered to be at a steady state with respect to an operation variable if that variable does not change with time. Such a process is called a steady-state process.
Say that Chris has a drum of orange juice with a hole in the bottom of the drum. Jeff's job is to use a hose and keep filling the drum with orange juice. If the hose is discharging the same amount of orange juice into the drum as is draining out, then the orange juice level in the drum would not rise or fall. When the orange juice level is constant it would be considered to be at steady state. This can also be applied to temperature profiles.