Judging from the CoachParrot tables (maybe you know what they are), in a base offence, it's based predominately on passing, partially off handling, with a minuscule driving component sprinkled in. Like 80% passing, 19% handling, 1% driving would be a rough estimate.
I guess it impacts your team by increasing offensive output. You get better shots and will have better efficiency. Some attributes like passing and handling also have a direct impact on some offences ratings. Motion for example, passing and handling hold big weights in the outside scoring rating there.