Assuming you're looking at this ArduinoStarterKit, it includes the aforementioned N-channel MOSFET (IRF520) and presumably guidance on how to use it. We'd need to know the current (or equivalently wattage) rating of your intended Peltier device to determine if that particular MOSFET is appropriate for the application.
alas, the IRF520 is not a low lever MOSFET and requires a second device, another FET or a transistor.
the IRL530 is a low level . the ' L ' is the difference.
MOSFET or FET is a device that kinda-sorta acts like a switch.(and can be used for other things)
a ' P ' type or P channel or PFET connects to the power side and you connect your motor to that then to the ground.
an ' N ' type or N Channel or NFET connects to the ground and you connect your motor to power then the FET.
N type are easier to use, more common, cost lest and you can find them easier. much more popular.
low level or logic level means that you only need 5 volts to make it work. the IRF version above needs the same voltage as the power supply to the motor. if your power supply is 12 volts, then you need to feed it a 12 volt signal to turn it on. not so easy without more bits.