The main motive for abduction can be to get a ransom or some other advantage from another person - say, to stop a politician being awkward by threatening and torturing his or her daughter.
It can be to get information from or intimidate the captive - or get her out of the way permanently and send a message to others.
There's also abduction with the aim of selling her into slavery or keeping her to earn money.
The main motive can be pleasure, for example to rape her. There's also accidental abduction: a cop jumps on a getaway car or surprises a robber and gets added to the loot; an honest subordinate surprises her boss in illegal activity and is taken to silence her. Of course, one case can involve several motives!
As for the circumstances, there's a big difference between abducting someone under guard and finding that an intelligence officer, policewoman, journalist or whatever is undercover in your organisation: once you've found she's a spy, she's yours.