Inherent behavior is behavior that an organism is born with and does not have to learn through experience.  Inherent or 
hard wired behavior may be a side-effect of prenatal and neonatal development processes.  It may also be a side-effect of adaptation processes.  The phrase encompasses reflexes, involuntary motions, and instinctive behaviors.
Some examples of inherent behavior include affinity to food triggered by hunger and scent (
alimentary), breathing, hunting activities, and many of the behaviors associated with procreation, among others.  There are also many inherent behaviors associated with avoidance, such as the pulling away from noxious scents, or blinking when a puff of air hits the cornea.
Responses of an organism caused by inherent behaviors are called 
unconditioned responses.  The stimulation that triggers inherent behavior is called 
unconditioned stimulus/stimuli (US).
Inherent vs Intrinsic
The term 
intrinsic behavior is sometimes used (informally) as a loose synonym for inherent behavior. The word 
intrinsic generally means behaviors or characteristics which are an essential part of the thing to which it is being applied, and can be applied to non-biological things.  For example, the C programming language includes 
intrinsic data-types, such as integers.
The word 
inherent differs, in that it generally applies to behaviors and characteristics that are 
inherited from a parent, or ancestor (often, but not necessarily, by a biological organism). As stated, the parent providing the inherent feature, attribute, or characteristic does not necessarily have to be biological. For example:
-  "An inherent feature of the assignment operator is its ability to produce an exact copy of a value or string.".
To contrast this, consider the statement:
-  "The ability to inherit functionality from parent classes is an intrinsic feature of object-oriented programming languages."
 
Here's another one:
  -  "Joe's blue eyes are an inherent feature."
  
-  "Iris color is an intrinsic characteristic of the human eye."
  
-  "An Iris's color is an inherent attribute. (full circle)
 
The word 
"innate" should probably also be considered here, for completeness. It, generally, means some feature, characteristic, or attribute, with which a thing is born. It usually carries the implication that the thing is alive, but there are exceptions. For example, the concept of "birth" can be used metaphorically.
Paper Trail:
The first seven synonyms for 
inherent listed in the Oxford Dictionary and thesaurus (American edition) are: 
"innate, connate, inborn, congenital, inherited, hereditary, inbred".