Remission refers to a shrinking of cancer. Doctors categorize remissions based on their extent. If after treatment, there's no evidence of the cancer on any tests, including blood tests and scans, doctors refer to this as "complete" remission. If the cancer is smaller but doesn't disappear completely, it's called a "partial" remission.
People who achieve a complete remission may be cured of their cancer. But there is still a chance that the cancer will return. This depends on the type of cancer and how far the cancer has spread. In people who achieve only partial remission, the cancer nearly always regrows.