A microcontroller can only do one thing at once. You can however use a timer interrupt to do steps of your program at regular intervals.
So, you have a timer interrupt that fires every one second. Each time it does, you update the 60 LEDs using one function.
You also have one or more counters that get tested / incremented every second. One of them can count the seconds and cascade to count minutes, hours, etc.
When the minute counter hits 60, you can clear it, advance the hour counter and update the 12 LEDs using another function.
I've simplified it a little, but hopefully you get the general idea.