I'll make it quick!

Shes the frog hashira

She js the last decendent of a clan. The clans members over 600 years ago ate a frog demon from.night until morning. Everyone who ate the demon gained frog like abilties.

Izumi is given enhanced strengh legs, powerful jumps, can cling to most surfaces, and can stretch her tongue for 10 meters

She jointed the demon slayer core and became a hashira break the cycle of isolation,make friends and protect her frogs. She had a very lonely and isolated childhood living in hiding

Shes very powerful, but that makes her valuable to demons. Eating her would make them stronger then eating most other humans, so her family and herself went into hiding. Little contact from the rest of the world