10mm in total or 10mm per side gives 20mm total?
The impact is that your car will increase its tendency to understeer if all else stays the same and only adding track-width on the back.
Similarly if you add only to the front and not the back and all other settings stay the same, then your car will be less likely to understeer (and more likely to over-steer).
Keep in mind that wheel spacers that widen track will always put some extra strain on wheel bearings and also on wheel studs / bolts.
The additional track width you mentioned, be that 10mm or 20mm total, isn't going to make much difference on daily driving, not should it present any major issues for bearings or studs/bolts.
If using spacers of 25mm plus per side you will need to look at it much more closely RE bearing capacity and stud/bolt tensile sheering values... and also if only applying to front or back at those values you will start to notice over/under steer impacts.