FPGAs and microcontrollers, like the Arduino, are very different devices. With a microcontroller you write software. That software gives you control of the the built-in peripherals, like IO pins, serial ports, or analog to digital converters. The biggest limitation of software is that you can only do one thing at a time!
With FPGAs you are not creating software. You are designing the hardware! Instead of writing code to run on a fixed processor with fixed peripherals, you get to design your own circuit. If you really want to you can even create your very own processor and write software to run on it!
A huge benefit of working with FPGAs is that every element of your design runs independently of each other. That means one part of your design can be reading in some serial data, while another part is controlling a servo, while another is reading some sensors, and yet another is controlling a display.
With a microcontroller you can often be limited by the built in peripherals. There is a set number of serial ports, PWM pins, or maybe you can't use some components, like a camera, because you can't interface with them fast enough. With FPGAs every pin has the potential to become whatever you need it to be. Do you need 84 PWM signals to control a lot of servos? The FPGAs have you covered. What about a bunch of serial ports or controlling a big LED display? You're covered there too. Since you are designing the hardware, you are deciding what each pin will do!