To pull strings is to use private influence to get something arranged. He pulled strings, pull a few strings, somebody pulled strings.
It implies a favour outside the proper process, which is why it is an accusation as often as a boast. The image is a puppeteer, and the related phrase for the person doing it is the puppet master.
1phrasepull stringsTo use private influence to get something arranged.
“Her father had to pull strings to get her an interview at the bank.”
pull strings is an influencing.
From the image of a puppet show, where the figures are moved by strings from above.
Suggesting a puppet show, where characters are moved by pulling attached strings.
Etymology from Wiktionary, CC BY-SA
Practised in Idioms