What is the definition of cognitive task?

Cognition--from which "cognitive
task" derives, is the scientific term that essentially means "the process of thought." 
Cognitive tasks therefore, are the actions which help define
cognitive thought process.

Usually the term "cognitive
task" is used in the context of "cognitive task analysis."  This is the process of
analyzing or testing what level of thought process a person has reached or is using to
solve a specific problem.  You might look at a toddler, for example, who touches a hot
iron and gets burned.  If this toddler learns not to touch the hot iron again, and
actually avoids it, he has demonstrated the cognitive task of understanding the iron
will hurt him and not to touch it.

In elementary education,
for example, it is common to measure cognitive tasks in subjects like mathematics. 
Addition and subtraction are learned and understood through a series of cognitive tasks
which build on one another.  A 1st grader might be able to handle physically counting 3
objects, adding one to the pile, and counting 4 as the result.  Gradually, the physical
object will also be represented by number symbols, and the understanding will shift from
the physical addition of one object to the pile, to the mental understanding that
3+1=4.  Each step in the process of learning 3+1=4 is a series of cognitive
tasks.

Many cognitive tasks are linked directly to short
and long term memory.  Others are developed physically (as though a process of motion). 
Humans learn and build understanding though hearing, speaking, and doing.  One theory
utilized in elementary education (and even higher) is the idea that blending these three
learning styles/techniques as much as possible allows students to experience and attempt
multiple cognitive tasks, providing the most opportunity to establish
understanding.