This is the power board. It's a separate board because it has 120 volt power running through it. Note that the path from the hot terminal through the triacs and to the output terminals are specified to carry up to 750 watts of power, so they're going to need to be very wide traces on both sides of the board.
The triacs are also going to need fairly substantial heat sinks. Even more so because they're going to be in proximity to the actual heated space of the oven. I think we can safely assume an ambient temperature of 50 degrees C, at least. The triac data sheet says that at the design current, we can expect it to dissipate 10 watts of thermal energy. The heatsinks I've ordered have a 5 degrees C per watt rating. Combined with the triac mounting terminal spec, the online calculators I've seen suggest that this ought to be a combination that should be acceptable.
The power board is a separate board so that it can be built-in to the oven. The two isolator input lines and ground can safely be routed out of the oven to the controller board, along with the thermocouple cable.
The three large terminals on the schematic are actually in the SparkFun electro-mechanical eagle library. They're #4 holes designed to be electrically connected. #4-40 hardware will be used to attach QD male connectors directly on the board. The QD female connectors on the wires of the oven will plug right in.