Hello, I hope the following is of assistance.
The lights you refer to are daytime running lights (DRL) although your car is a 2008 car DRLs became mandatory in 2011 which is why you see new cars with the LEDs on during the day.
For some reason this feature was fitted to some Mazda models in 2007/8 but then removed again in 2009. The feature can be disabled by replacing the headlamp relay from part number GS1G67890A to GS1E67890A but this relay is quite expensive. The relay is located up behind the glove box. Given the cost of the relay unless you have any real reason for turning the lights off I would leave it as it is.
I hope this helps, let me know if I can assist further.