Daemati are faeries that have the ability to walk into another person's mind. They are able to read, influence, and even shatter someone's mind, depending on their training and power.
When Feyre is rescued by Rhysand on the night of Calanmai, they make a small connection. Rhysand uses his Daemati powers to read Feyre's mind and deduce that she is lying about her name in Tamlin's residence when he discovers she was being glamoured by Tamlin.
He later uses his ability in Under the Mountain to interrogate a faerie from the Summer Court and kill him, as a mercy.
When Rhysand saves Feyre from her wedding with Tamlin, he finds out that she got a piece of High Lord's powers. He teaches her to use a mind wall to shut him or any other daemati out of her mind.
For the first time she uses her powers in Spring Court when she accidentally enter in Lucien's mind. Then she does that again, but in Velaris, with Rhysand's mind and for the first time since Amarantha she sees how shallow and broken and starved she looks. She asks Rhysand is he doing some king of trick but he says no.
At the end of ACOMAF she uses them again to tell Rhys to take her sisters away to Velaris and keep them from Tamlin and the rest who might hurt them.
She uses her new skills to protect Lucien and Tamlin from them, and because she was so focused on that, she didn't realise that they were slowly weakening her powers by putting faebane in her food and drink.
Feyre uses her daemati powers when she sees Lucien and Ianthe. With her powers she forces Ianthe into shattering her own hand with the rock.