This is a topic that get discussed very frequently here. A search on the keywords FAK and EDC with the date range set to all dates and all forums will turn up an abundant amount of reading for your pleasure and edification.
Most carry atleast gloves, bandaids, moleskin, pain-killers and a few other meds. Some carry CPR masks if they have the training to use them. There are doctors, paramedics and EMT's as members on this site so there are a lot of very informed posts on the details of different gear.
A good start is to get one of the "Hikers First Aid Kits" from your local wallyworld. Follow that up with a decent "first responders" course at the local American Red Cross or St. Johns Ambulance (depending upon what is available) and add whatever they train you to use. Right about then you will have the training and desire to carry way more than would easily fit in your pocket and you will have much more specific questions to post here.