Often during a TV show or a movie you will hear someone saying 'they have left behind a breadcrumb trail' when talking about hackers or someone accessing a computer system. A breadcrumb trail is simply a navigation path so in the context of a TV show talking about hackers, it's just another way of saying they have left a record of their navigation.
Breadcrumbs are used is virtually every computer language. You see them being used by your Windows operating system, many websites use them for easy navigation. To help you understand, here is a visual breadcrumb trail that you've probably seen in many places without knowing what it is:
Home >> portfolio >> Gallery >> Photos >> Me.jpg
The above is the most simplest way to explain a breadcrumb. Try to think of it as a hirachy of pages with the first page being 'Home' which leads onto the portfolio page, then onto the gallery page, next onto the list of 'Photos' and finally the photo itself. One page leading onto the next, the above visual presentation of this is a breadcrumb trail.
If you use the Windows operating system, you will see a breadcrumb trail at the top of any window you open. I've just opened a folder on my desktop called 'trainers' and at the top of this folder window here is the navigational breadcrumb trail:
C:\Users\Richard\Desktop\Trainers
Computer programmers will always use a breadcrumb to tell an application where to go and how to get there.