Literally: extensive – pull – to the side – evidence
Alternately: As one member or side of a dispute or controversy, supporting one’s case by citing an extensive body of examples or material. Presenting a solid, perhaps overwhelming, amount of evidence.
Notes: This practical yojijukugo is a compound of compounds; 博引 refers to using a wide array of materials or examples to explain something; 旁証 refers to presenting evidence.
Note that the 旁 character is rare these days; it can be (and often is) replaced with close relative 傍 without any change in pronunciation or meaning.