Your data remains on your desktop. Trifacta Wrangler stores all of your data on your local machine and uses your local machine to process your transformations and save a result file.
Where is my data stored in the new cloud wrangler ? Is my data secure ?
Uploaded user data and wrangled results are securely stored in S3 buckets hosted by Trifacta.
I should be clear: my response above refers strictly to the cloud version of Wrangler, not the desktop version which Connor covered.