What is the “System Interrupts” process in Windows?

"System interrupts" is not a process in the traditional sense, but is present to try to explain to the user that the computer is spending 1.5% of its CPU resources processing interrupt requests. Interrupts occur below the OS level, so they are not associated with any particular process.

Interrupts (IRQs) exist so that the hardware components of your system can tell the CPU things like "an error occurred", or "the data you requested is now available", or "this device would like to send data". Any time a device or piece of software needs to tell the CPU something about the task it's performing, or needs to instruct the CPU to do something, it raises an Interrupt, which the CPU receives and handles. When this happens, the CPU immediately stops what it is doing such that it processes the interrupt.

When viewed as a process, another related item are Deferred Procedure Calls (DPCs), which are OS functions called either directly or indirectly in response to a raised interrupt, in an asynchronous manner. By adding the System Interrupts and DPC processing together, you can generally estimate the amount of resources in use responding to IRQ handling.

There are good interrupts and bad ones. If you are spending a lot of time on interrupt processing, there is a good probability that at least one piece of hardware is failing. On the other hand, lots of hardware use IRQs for timing and other valuable purposes. For instance, the PCI bus uses IRQs to control what device is using the bus at any given instant, so that every device shares the bus efficiently.

At 1.5%, everything sounds normal to me.

“System Interrupts”—also known as “Interupts” and “IRQs”—are operating system level processes that manage how hardware communicates with your system. As explained here on Wikipedia:

In systems programming, an interrupt is a signal to the processor emitted by hardware or software indicating an event that needs immediate attention. An interrupt alerts the processor to a high-priority condition requiring the interruption of the current code the processor is executing. The processor responds by suspending its current activities, saving its state, and executing a function called an interrupt handler (or an interrupt service routine, ISR) to deal with the event. This interruption is temporary, and, after the interrupt handler finishes, the processor resumes normal activities.

So it is a necessary part of your core system setup. And if the CPU usage shoots through the roof, it simply means there is some issue with your system communicating to hardware.