According to the Wired report, your iOS device records what you say to Siri and sends that clip to Apple's servers for analysis. As part of the voice recognition translation and response, Apple assigns a set of random numbers to the clip to identify the user from which it originated. This number is used during the back-end voice processing to make sure the response is sent back to the correct phone.
Apple stores this clip along with the random number for six months. After six months, the number is stripped from the file and the file is kept for up to 18 months.
The practice of storing anonymized data for several years is common among tech companies that handle large volumes of data. Wireless carriers, for example, keep select user data like text message history for up to five years.