This is the 1342nd most frequent Polish word.
planów
"Plans" (genitive plural form of "plan").
Here, 'planów' is the genitive plural form of 'plan', used after the negation 'nie mam', which requires the genitive case.
Nie mam dzisiaj żadnych planów.
I don't have any plans for today.
In this sentence, 'planów' is not used; 'planami' (instrumental plural form of 'plan') is used because it's required by the verb phrase 'pracują nad'.
Oni pracują nad kilkoma nowymi planami.
They are working on several new plans.
'Planów' is the genitive plural form of 'plan', used here to indicate possession or relationship ('part of the plans').