How does Siri translate all that on my phone? How does it work? I heard it sends all your data off to the internet to be translated. But it seems like it's integrated into my phone.

Does it run on the phone or on the internet?
Siri makes use of NLP(Natural Language Processing) - NLP computing takes significant resources and while the iPhone may be powerful enough to process them, it's likely to drain the battery. 

For this reason, Siri application records your commands on your phone &amp; sends it off the servers for processing. The results are returned back to the phone &amp; does the commands. 

So to answer, yes, it's part-phone, part-Internet service &amp; it does send data to Apple's servers.