Trigger

Understanding Trigger Context Variable

When I started my carrier as Salesforce developer.when I wrote my first trigger code, I always use to hear "first understand Trigger.new and Trigger.old"(Trigger context variable) from senior colleague in my team. Then I started searching for what trigger.new, trigger.old and other context variable will return in trigger, whether there is any practical experiment for this, but I didn't get any. 

This is only one Salesforce site helped me to understand theoretically.