The chordate trait you are describing is more precisely termed post-anal tail. It is one of the basic characteristics of all chordates, along with, among others, pharyngeal pouches, a hollow dorsal nerve tube, and a notochord. Two other traits are less commonly considered chordate traits: segmented body musculature and a thyroid gland or endostyle (the latter particularly controversial).
These characteristics are present in all chordates at some point during their ontogeny. These traits are shown below.
We can see these most clearly in embryonic forms. For the post-anal tail: in humans, there is a short "tail" that extends past the anus (end of the yellow tube). This tail does not typically persist for very long. Similarly, the notochord is absorbed into the vertebral column, and remnants of the pharyngeal pouches are not externally visible.
The key phrase is "at some point during development." Non-embryonic humans don't have a tail, but that doesn't mean humans are not chordates.