What is this component called?
Welcome to the Electronics SE. 

The device you picture is a thermal fuse (aka thermal cutoff). It is not what is causing your problem. All it can do is cut off the power, and it does that only once and stays open (there is a bit of material inside that melts and the device opens up). It must be replaced with a similar type with the same melting temperature (usually marked on the side). It's purpose is to keep your house from burning down. Yours is probably fine or the machine wouldn't be blowing your breaker. Here is a datasheet showing typical models.



Most likely your heater has shorted internally, perhaps to ground. That would typically mean it's unrepairable economically because a replacement heater would be too costly, at least for a cheap coffee maker. If it's a $2K Faema commercial cappuccino maker, then of course it will be repairable. There are other possibilities such as a bad MOV or capacitor if there is electronics in the coffee maker.  

Be extremely careful working with this, if the heater has shorted to ground, a faulty ground wire could cause mains voltage to appear on the housing of the kettle, which could result in a (possibly fatal) electrical shock to someone touching the housing. 

The ground connection and the thermal fuse are both safety considerations that are not involved in actually boiling your water or controlling the normal shut-off, they are there to make sure a failure inside the coffee maker does not result in damage or injury.