With a constant load, DC (direct current) has a constant current and voltage.
This is as opposed to AC (alternating current) which, with a constant load, has an alternating current and voltage.
It's essentially a description of the current and voltage's relationship to time. For DC, the frequency is equal to zero, not changing in time. While AC has a frequency equal to not zero, it changes with time.
Relationship between Voltage and Current
The key to the relationship between current and voltage, is the load, or resistance. This comes from Ohm's Law, \$V = IR\$. As you can see, if \$R\$, the resistance is constant then voltage (\$V\$) is equal to the current (\$I\$) times a constant coefficient. Set \$R = 1\$ and the relationship is quite obvious.