Equality -- What a word.
For me, equality can be summed up with something I wrote recently (Warning: F-bomb dropped once, but I think its the only non-family friendly word in there...)
https://fierymamarow.deviantart.com/art/Fight-for-Us-701107033BUUUUUT in short what it says, is that to me, I don't want to have to wake up in the morning and TELL myself that I'm not a freak, and that I deserve the rights that every human should have. I don't want to feel like this country I live in hates everything I am, and I that I don't deserve anything.
For me, Equality means not being afraid to be me. When I walk out my door, I want to be able to expect that if I apply for a job, its based on my qualifications, skills, abilities, etc. Not the color of my skin, my gender, my sexuality, my hair color, my height, my mental illness, etc. If I can do the job, that's what I expect to be judged on. If I were to divorce and remarry, I expect my government to respect that love knows no bounds. Religion, that's a different story, but I live in a country where religion and state are not supposed to be synonomous. I expect if I go into a grocery store, for the cashier to take my credit card to pay for my oranges the same as he would the guy in front of me. I expect not to be afraid to use the bathroom. I expect that if a crime is committed against me, I will get the same justice a cis-white-christian male would. Those are just a few examples.