How did 'repraesentāre' semantically shift to signify 'standing in the place of another'?
To wit, how does "present again, bring back" (in repraesentāre) semantically appertain to the notion of 'standing in the place of another'?
English borrowed represent from Latin repraesentāre, which meant ‘present again, bring back’, hence ‘show’. It was a compound verb formed from the prefix re- ‘back, again’ and praesentāre, source of English present. The notion of ‘standing in the place of another’ is a post-classical development.
Word Origins (2005 2e) by John Ayto, p 421 Right column. Ayto doesn't expound this semantic shift.