A Baron is the lowest rank of nobility (something someone probably tried to teach me long ago via historical context, but I mostly remember now due to fictional stories). The "upstart" bit is meant to imply that his father wasn't born into nobility, and was instead made a baron at some point.
In short, he's fifth in line for the inheritance of a Baron who was previously a commoner. Or so he claims while performing this task, anyway. For all we know, he's the first son of a Duke.
I'm not entirely sure if his sister is simply giving this task her all, or if she just really does want a horse. I'd believe either.