The story behind the Shinso:
Long before the events of Rosario + Vampire, there was a very powerful vampire named "Shinso". Those who inherit his power by absorbing his blood are given the title of "Shinso".
One Shinso named "Alucard" tried to take over the world, leaving fire on the entire continent for seven days. Another Shinso and her two companions stopped Alucard, the oldest existing vampire. The three who stopped Alucard later were given the title "Three Great Dark Lords". To this day, the corpse of Alucard is being watched over by the Three Dark Lords and the Shinso that attacked Alucard: Akasha Bloodriver.
Ever since Alucard's defeat, his body has been kept in hiding never to be seen again and the title and identity of the second Shinso seems to be kept a close secret for her safety and to prevent the birth of another Shinso like Chapter 32 Season 2, it appears Alucard is awakened when Moka shows her power of Shinso.
Now the only confirmed Shinso who still survives in this world is Akasha Bloodriver, but, never appeared in Yokai Academy or in the presence of Moka. Her face looks like the "Outer" Moka, although they having different personalities she's always appeared with a smile and pretty face. When Moka leaves her home, she didn't come to say goodbye but it is imagined she cries in her heart for letting her only daughter leave.
When Moka was born she was already on the verge of death, so to save her, Akasha, transfused as much of her blood as she could to save her, the end result her shinso power transferring to Moka and saving her. So powerful was her love for Moka that she had her rosary made to seal her shinso power, just in case. As fate would have it, Moka went berserk upon seeing her mother cut in half by her sister and awoke, also waking Alucard. To save Moka, Akasha gave her life to activate the seal putting the outer 'Fake' Moka into place and was then absorbed into Alucard to "seal him from the inside".
Shinso Blood:
The Shinso Blood by the way has similar properties to Vampire Blood but it is much more powerful. It could be considered a very dangerous weapon depending on how you use it. The blood must be transferred you cannot however inherit this blood, it must be transferred from the person who has the blood. In this case you could say it must be injected to your body so technically speaking Tsukune currently has Shinso blood inside his blood stream.
Powers:
It is shown that Shinso possess great strength and insane regenerative abilities, seen in in chapter 31-33 when Akasha was cut in half by Akuha yet fully regenerated, stating she had a 'tough body'. It is also speculative that Shinso possess great speed, but it has yet to be confirmed.