Lifesteal is an all new ability coming to Hearthstone with the launch of Knights of the Frozen Throne. A card with this keyword will heal your Hero for any damage dealt. While the keyword itself is new, the effect is not. "Damage dealt by this minion also heals your hero," is the antiquated way of saying it and this is actually the exact same effect as Mistress of Pain which was part of Goblins vs Gnomes back in December of 2014. More recently Wickerflame Burnbristle had the same card text with Mean Streets of Gadgetzan in December 2016.
To make the keyword clearer, Blizzard has given cards with its effect a broken heart underneath their art when they're on the battlefield.
As has always been the case, it does not matter whether or not the minion with Lifesteal is attacking or not, any damage it deals heals you.
Donais has described Lifesteal as a "smaller mechanic" like Poisonous from Journey to Un'Goro. He says they're very careful about Neutral cards with this keyword because of what that would mean for Warlocks with Life Tap.
Spirit Lash is the first spell ever to have this effect.
If Betrayal is cast on a minion with Lifesteal, it will heal the owner for all damage dealt.
While Auchenai Soulpriest and Embrace the Shadow currently combine for a deadly combo with these kinds of cards, Blizzard is changing this interaction with Frozen Thrones. Currently, the one damage dealt registers as a heal but it actually does damage, causing you to heal again which then causes another point of damage. This leads to the owner of the minion being OTK'd most of the time. In an upcoming update, this cycle will be limited to a single occurrence.
Cards With Lifesteal
Released Before Frozen Throne
Frozen Throne Commons
Frozen Throne Epics
Frozen Throne Legendaries
Knights of the Frozen Throne
Want to learn more about Hearthstone's upcoming Knights of the Frozen Throne? Head on over to our expansion guide.