Google translate says piano is "plan", "floor", etc. However, I've heard that "piano, piano" could translate to "little by little". Is that an accurate translation? Does "piano" mean other things than just "floor"?
Piano is a very peculiar word in Italian because it has several meanings, all deducted by context:
Softly\Slowly\Quietly\Soft\Slow\Quiet (Adv\Adj.) as in your case: "Ci siamo conosciuti piano piano". We knew each other little by little. "Parla più piano!". "Speak quieter!"
Flat (Adj.): "La strada era abbastanza piana". "The road was quite flat".
Flat\Plane land (Noun): "La casa era costruita in piano". "The house was built on flat land."
Plane (Noun): As in mathematics: "Piano cartesiano". "Cartesian Plane".
Piano (Noun): As in the instrument (better, pianoforte): "Lei ha suonato il piano". "She played the piano".
Plan (Noun): "Abbiamo un ottimo piano". "We have a great plan".
Floor (Noun): "Abitare al primo piano". "Living on the first floor".
Slow Down! (Adverb): "Piano!". "Slow down!". This is true both for the figurative and the literal meaning. You can also find the form "Vai piano!" for the literal and the form "Vacci piano!" for the figurative.
It could have several meanings:
Abito al secondo piano
Non correre, vai piano!
Avvicinati piano piano (little by little)
Piano (musical instrument)
Suoni il piano? (also "pianoforte")
Qual è il tuo piano? (What's your plan?)
My cousin in Italy always said, "piano e piano" as I struggled to speak Italian. It's an italian phrase meaning little by little or step by step. "Pieno" means full.