This song is called "Bella ciao" (Goodbye, my Beautiful-->my LOve) and it's a traditional italian song. The music was original created in the 19th and was a popular song sung by the mondine (women working on the rice fields). The famous version is the one you posted and it's our best song of the Resitenza (Italian Movement against Fascism during the II World War).
Una mattina mi son svegliato
One morning I woke up
o bella ciao, bella ciao, bella ciao, ciao, ciao,
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
una mattina mi son svegliato
one morning I woke up
e ho trovato l'invasor.
and I found the invader (that means the German troups).
O partigiano, portami via,
Oh partisan (I guess it's a litterary translation: partigiano means Italian fighter of the Resistenza) take me away
o bella ciao...
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
o partigiano, portami via
oh partisan take me away
che mi sento di morir.
that I'm feeling like dieing
E se io muoio da partigiano
And if I die as partisan
o bella ciao...
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
e se io muoio da partigiano
and if I die as partisan
tu mi devi seppellir.
you must bury me
Mi seppellirai lassu in montagna,
You will bury me over there, on the mountain
o bella ciao...
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
mi seppellirai lassu in montagna
you will bury me over there on the mountain
sotto l'ombra di un bel fior.
under the shadow of a wonderful flower
E la gente che passera,
And all the people passing by
o bella ciao...
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
e la gente che passera
and all the people passing by
dira "o che bel fior!"
will say "what a wonderful flower!"
You're missing some words, here there are:
E questo è il fiore del partigiano
Ad this is the flower of the partisan
o bella ciao...
goodbye my Beautiful, goodbye my Beautiful, goodbye my Beautiful, goodbye
morto per la libertà
dead for our freedom
e questo è il fiore del partigiano
and this is the flower of the partisan
morto per la liberta
dead for our freedom