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.

The term is first recorded 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 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.