An Allomantic Savant is an allomancer who has flared and/or burned an allomantic metal for vast periods of time, causing changes within his/her physical body. Savants have an greatly increased reaction to burning metals.
A Tineye Savant's senses for example are pushed well beyond what a normal Tineye can attain. Most Seekers become Bronze Savants without even knowing. Their range of Allomantic sensitivity is drastically increased. Becoming a Pewter Savant is dangerous, as there is an enormous change to become addicted to the metal, as your body becomes more and more reliant on pewter over time. Pewter Savants also push themselves to a point where they cannot feel exhaustion or pain, and usually end up killing themselves before the Savant process can be completed.
Spook, a Tineye, is the only Savant introduced and named in the Mistborn Trilogy. One could speculate that the inhabitants of the Lord Ruler's soothing stations were also Allomantic Savants, as they burned their metals day and night for years. While becoming an Allomantic Savant may have great rewards, those same rewards may become dire consequences.