Seraphina is Hebrew, meaning "burning ones" or "fiery ones." It is the Latin and feminine form of the word seraphim, which are the six-winged highest ranking angels of God. The meaning is intended to describe these powerful fiery-winged angels, not the feathery-winged ones we typically think of. These angels were warriors.
Despite the fact that Jennifer Garner and Ben Afleck used this name for one of their daughters, the name is still quite rare, even though it is one of the most looked-up baby names. It was also the name of a 13th century saint (technically four, I believe, but the other woman was born named Sveva and two were male - Serafino and Serafim), being very popular in medieval Italy.
There are a few different ways to use this name: Seraphina, Serafina, Saraphina, Sarafina, Seraphine, Saraphine, and Serafine. In 2010 there were 12 baby girls named Sarafina, 9 Saraphina, 6 Seraphim, 5 Serafima, 79 Serafina, 107 Seraphina, and 17 Seraphine.
Seraphina has a range of nicknames, from Phina to Fifi, Sera to Nina, depending on how the full name is spelled.