Yes, a Dual Inline Package. Guessing what things are on the pic:
If this works with your (unspecified) motor and battery (9V?), I'd guess that the transistor-looking thing is enough of a motor driver to handle your motor, and the rest of the circuit is doing your 10-second delay. (With the resistors and capacitors, I'm just guessing it is some sort of 555 circuit) If you plan on doing the delay and control with an Arduino, that board picture indicates that a simple transistor driver like the top left one here would be adequate:
But if building one of those is difficult, you could buy a more robust motor driver breakout board such as one of these from Pololu: