This is a great question!
To 'deadname' a trans/gender diverse person is to call them by a name they no longer use. (Typically this is their birth name). Sometimes a deadname can still be an individual's legal name, but it's not the name they use, or the name that 'feels right'.
You can also use 'deadname' as a noun. For example, as a general rule, it's never okay to ask someone about their deadname.
Lots of trans/gender diverse folks have a rough history with the name they were given at birth because directly links them back to the sex they were assigned at birth.
In many (but not all!) cases, trans and gender diverse people experience dysphoria, which basically means their physical body and their internal identity don't match. Dysphoria can lead to a lot of really tough emotions and psychological damage - like becoming triggered and developing severe anxiety, depression, and far too often, suicidal ideation. When I say 'triggered', this isn't something to take lightly. Being triggered isn't simply being offended. It's not a term that should be used casually.
When someone is triggered emotionally, it often comes with pretty major physiological changes. Sometimes your breathing can become difficult, your heart races, you become shaky or naueated, etc. It's a legitimate experince not dissimilar from the reactions of first responders or military folks with PTSD. Trust me, it's scary stuff.
In my case, I was assigned female at birth. It always felt super weird and I didn't know why. It wasn't until I was nearly 30 that I learned that being transgender was even a thing! Living in very rural Alberta, Canada I'd never heard the term before so it was an absolutely foreign concept to me. But oh boy, did it ever answer a lot of questions and explain a lot of the feelings I had growing up.
I was given a very feminine name when I was born. I don't blame my parents for that at all. They called it as they saw it! ;)
But my deadname wasn't something I was comfortable with so I legally changed it to B. Yup, the name on my birth certificate and driver's licence is literally just the letter B. I don't even have a middle name.
I'm basically Cher.
Again, this is turning into a very lengthy babble about a pretty simple concept. Do I really talk too much?
A deadname can be a powerful weapon. A simple word that can be incredibly damaging when misused.