This is the 13603rd most frequent Polish word.
planecie
"Planecie" means "planet" in the dative or locative case in Polish.
Here, 'planecie' is the locative case of the noun 'planeta', used after the preposition 'na' to indicate location on the planet.
Na naszej planecie żyje wiele gatunków zwierząt.
On our planet, there live many species of animals.
In this sentence, 'planecie' is also in the locative case, governed by the preposition 'po', which introduces the idea of moving around or across the planet.
Chciałbym podróżować po całej planecie, odkrywając różne kultury.
I would like to travel across the whole planet, discovering different cultures.
Again, 'planecie' is in the locative case, serving to describe the location where the situation pertains — the planet.