A vitality starter, from my reading and practice, is a starter that is made on the day of brewing. It takes less wort than a traditional starter and the purported purpose is to pitch the yeast into a smaller starter of well oxygenated wort to allow the yeast to adapt to the new environment and start building the materials they need for rapid reproduction. The yeast uses the oxygen in the wort to make sterols which are used to strengthen the cell walls, an action which is needed for repeated and rapid budding and cell replication. Some sources compare it to 'proofing' dry yeast, but it really comes down to the health or vitality of the yeast cells providing enough nutrients to give a healthy fermentation.
In practice, I use both a traditional starter and a vitality starter. I save about 300 cc of wort from the boil, which I use to check the gravity and pitch the appropriate number of yeast cells needed from a traditional starter or a new yeast packet. It usually takes about 4 to 6 hours for that to start showing signs of activity and start building a head of foam on the top. At this point, I pitch it into the carboy, which has been sitting in my fermentation chamber stabilizing to my preferred pitching temperature.