As nvoigt says, you can use the home licence as a visitor for a set period of time. In the UK and Canada it is 60 days. Any longer and you need to exchange the licence for the country's. Normally this is a straight exchange, no driving is tested (although they may do a vision test).
When you return to your original licenced country, you use the foreign one for the grace period again, then have to do the exchange the other way.
The rationale for this is simple, if you can keep both, it'd be easy for you to pull out your foreign licence if pulled over, and have any offence lost (these things rarely go back internationally).
For example, in Ireland there was an arrest warrant out for Ireland's worst foreign driver, a Polish man named "Prawo Jazdy"
What they eventually found was that the officers had been recording the info from the foreign licence wrong and that "Prawo Jazdy" means "Driving Licence"
more details here:
BBC News -
The mystery of Ireland's worst driver