In addition to what others said (Pence reassuring the white evangelicals who had concerns and doubts about Trump) I would also like to point out that the Pence pick likewise reassured some of the powerful (conservative) elites in the United States that Trump would sign-on to their ideological agenda - or at the very least, not obstruct it.
Good point. Trump's con artist lies about him not letting people die in the streets due to no healthcare, being against wall street and not touching medicare made him much more palatable to the working class. The big down side is it must have scared the donors and think tanks to death, so Pence made a lot of sense to assuage the hard line ideological concerns they had.
