Trickery - double dealing. Also, more recently, sexual shenanigans.
This is one of those nonsense terms that was just made up as having an attractive alliteration or rhyme, like 'the bee's knees', 'the mutt's nuts' etc. The words themselves have no inherent meaning, although it is possible that 'hanky-panky' derives as a variant of 'hoky-poky' or 'hocus-pocus'.
The term is first recorded, in relation to its original 'trickery' meaning, in the first edition of 'Punch, or the London Charivari', Vol 1, Sept, 1841:
"Only a little hanky-panky, my lud. The people likes it; they loves to be cheated before their faces. One, two, three—presto—begone. I'll show your ludship as pretty a trick of putting a piece of money in your eye and taking it out of your elbow, as you ever beheld."
The second meaning, which I can't do any better for a definition than to repeat the OED's listing "Sexual activity or dalliance, especially of a surreptitious nature" has been with us since the middle of the 20th century, as here from George Bernhard Shaw's Geneva, 1939:
She: No hanky panky. I am respectable; and I mean to keep respectable.
He: I pledge you my word that my intentions are completely honorable.
See other reduplicated phrases.