Disposable diapers are pretty safe for both babies and adults to wear but they do contain chemicals such as ethylbenzene, toluene, xylene and dipentene in the manufacturing process.
The material that is used in the diaper to absorb the urine is called SAP or Super Absorbent Polymer which swells up when it comes into contact with urine, water etc.
Disposable diapers are made on massive machines that make thousands of diapers per hour and use things such as plastics, glue etc in the manufacturing process.