Also says they can wear their own clothes?
How would that work then?
It varies from prison to prison.
In some prisons you get issued with a mesh laundry bag, which is labelled, and you put your dirty clothes into it and hand it over to be washed. It gets washed and dried, still in the bag, and then handed back to you. The prison laundry is usually staffed by other prisoners.
Some more 'open' prisons might have facilities where you can do your own laundry in your own time, but I don't know how common that is.
In practice, it's also very common for prisoners to try to wash things like socks and underwear in the washbasin in their cell and drape them over a chair or bed frame to dry.
Wearing your own clothes, however, isn't something that's unique to remand prisoners. Loads of prisoners are allowed to wear their own clothes. They usually have a set number of specific items they're allowed to have. It depends what category of prisoner they are, what kind of wing they're on, how well they behave etc. The main restriction on clothing is that you aren't allowed to wear sports team tops or t-shirts with political or offensive slogans/images on them.
In terms of what people do, they fill their time one way or another. Reading, watching TV, playing cards or board games, going to the prison gym, writing letters home etc. There are also things like support groups etc and sometimes organised activities like art/drama groups.
Before anyone says 'Oh, that sounds all right' I can tell you now that it absolutely isn't, whether you're on remand or a convicted prisoner. I've visited some prisons (in a work context - I don't have a family of criminals or anything!) and they're grim as fuck.