The canonical-census v0.1 description is simply "canonical-census - send "I am alive" ping to Canonical." When looking at the Debian package source to this Python program, "Send an "I am alive" ping to Canonical. This is used for surveying how many original OEM installs are still existing on real machines. Note that this does not send any user specific data; it only transmits the operating system version (/var/lib/ubuntu_dist_channel), the machine product name, and a counter how many pings were sent."
When the canonical-census package is installed, the program is to be added to the daily Cron jobs to be executed so that each day it will report to Canonical over HTTP the number of times this system previously sent to Canonical (this counter is stored locally and with it running on a daily basis it's thereby indicating how many days the Ubuntu installation has been active), the Ubuntu distributor channel, the product name as acquired by the system's DMI information, and which Ubuntu release is being used. That's all that canonical-census does, at least for now. Previously there haven't been such Ubuntu tracking measures attempted by Canonical.
The good news for those concerned about privacy is that it appears for now Canonical is just interested in tracking the users of OEM installations -- those PCs that ship with Ubuntu by default such as from ZaReason, System76, and Dell. This information will obviously be valuable to both companies to see whether customers are keeping around their Ubuntu installations or just wiping them and just how often Ubuntu is being used on these systems (judging by the number of times that system reported to Canonical's server previously). For those not wanting to participate in this anonymous data gathering process, they could always sudo apt-get remove canonical-census.
The Canonical Census package can be found on Launchpad.net for those interested.