Does anyone know what kind of material this is?
Feels like hard plastic

How do you remove it?

 

Looks like dark epoxy or cement, often used to cover a proprietary device so it cannot be reverse engineered that easily. Hiding what devices they use is a common practice with some vendors.
It cannot be removed easily, not without damaging the board itself.

 

Sagar is correct about that blob of black epoxy. It is anchoring and protecting an open intgrated circuit. at least that is the standard application. But it might also be protecting a regular DIP IC. so in either case removing that material will destroy the electronic device it is covering.

 

As mentioned, there is most likely an integrated circuit under the blob. In many cases the integrated circuit is connected to the PCB by soldering the chip to the board or by bonding wires.

The black epoxy protects the integrated circuit from physical damage and the environment.

 

My much closer examination tells that these are the two PC boards from an "X-Box ELITE" controller, and so that black epoxy "blob" is hiding an IC device that they want to keep secret. So not only will messing with it destroy the board's function, in addition no replacement will be available.

 

Panasonic was one that came up with a method of IC encapsulation it is to serve and protect the device from environmental and physical damage. They can be made from epoxy or epoxy blends, silicone, polyimide or either solvent-based or room temperature vulcanizable.

 

Something some people may not know is that an IC, known to consist of many thousands of transistors, is susceptible to light. Light shining on junctions will turn them on. So that's a part of the reason why the blob is black. Actually color doesn't matter, but the "other" function no one has mentioned is that it also prevents the chip on board (COB) from being triggered by light leaks that would otherwise overwhelm the electronic circuitry.