The schematic below is an H-bridge , the high and low mosfets are internal to the two ICs on the right side, their datasheet is here. What is the purpose of the part on the left, which I googled to be a buffer IC, datasheet here. Is it for the sake of circuit protection? My understanding of using a buffer is limited, I have always assumed they where used in cases where something could not source enough current to drive something else, so you use a buffer with higher current sourcing capability. Is this correct and is this the case here?
It is a buffer and used because the drive source current at hdr P3 is not known. This buffer has almost no load on its inputs but can source +/- 8 mA per pin, even though the package has a wattage limit, depending on if you get a SOIC package or a DIP package. Maximum total current is limited to 50 mA.
That is more than enough to drive the H-bridge drivers. Speed limit for U1 is about 20 MHZ though 50 MHZ is possible with just 15 pF loads. Plenty fast for PWM if you are using that.