Spin a coil in a magnetic field and it generates a voltage, whether or not you meant it to. A DC motor's armature is exactly such a coil, so the moment it turns it generates a voltage of its own, and that voltage opposes the supply that is driving it. This is the back-EMF, also called counter-EMF, and it is the most important number inside the machine.

$E_{b} = V - I_{a} R_{a}$, read aloud E-b equals V minus I-a R-a. $E_{b}$ is the back-EMF in volts; $V$ is the supply voltage at the armature terminals, in volts; $I_{a}$ is the armature current in amperes; and $R_{a}$ is the armature resistance in ohms, winding and brushes together, usually a fraction of an ohm. The subscript a is for armature on both, and b is for back. It is Kirchhoff's voltage law round one loop: the supply is shared between a small resistive drop $I_{a}R_{a}$ and the generated voltage. In a healthy running motor the back-EMF takes nearly all of it, 90% or more.

Read the other way, $I_{a} = \dfrac{V - E_{b}}{R_{a}}$: only the DIFFERENCE between supply and back-EMF drives current. That is why a DC motor regulates itself. Load the shaft and it slows; back-EMF is proportional to speed, so it falls; the difference grows; more current flows and more torque arrives, with nothing commanding it. It is also why starting is violent. At standstill $E_{b} = 0$, the whole supply lands on that fraction of an ohm, and the current is $V / R_{a}$: often twenty times the running figure or more. Every starting resistor, soft starter and drive exists to tame that one instant.

The named trap is the sign. $V + I_{a}R_{a}$ is the GENERATOR's equation, where the machine pushes current out and its EMF must sit above the terminals. A motor takes current in, so its back-EMF sits below the supply, always. Units guide, they do not confess: amperes times ohms is volts, so every term balances, but the units are equally happy with the plus sign and will never tell you which machine you have.