What exactly is a Euler Bus?

[gbjensen]

To clarify those port types (please correct if wrong):

I²C (Inter-Integrated Circuit)

https://en.wikipedia.org/wiki/I%C2%B2C

Euler Bus has I²S ports rather than I²C. At least that's what the pin-out seems to indicate...there are perhaps some I²C ports on the Pi-2 interface...

Yes, there is an I2C bus at the Pi-2 interface pin 3 and 5. an I2C bus can be used for many DIY projects e.g. A/D or D/A converters etc. ets.