For AC on-off control you can use a relay (or solid stage relay). AC Dimming is more complicated. A relay isolates the AC from your low-voltage Arduino (for safety!) and allows a small voltage & current to control a larger voltage & current.
The relay coil (input-Arduino side) needs to be rated at 5V and less than 40mA. This is the power required to activate the relay. The relay contacts (AC output side) need to be rated for the AC voltage & current or higher. These are the maximum amount of power the relay can switch.
5V relays with AC power contacts are not that common, but if you search for “Arduino Relay Board” you can find boards with multiple Arduino-compatible relays.
Most solid state relays work fine with the 5V control voltage from an Arduino. (The output-side ratings are a bit more critical, and you can’t use an AC solid state relay with a DC load circuit.) Solid state relays can switch faster than mechanical relays, and they don’t make a “click” sound when they switch on & off. But they tend to be more expensive.