What does the use of 'verb 了 verb' indicate?
[verb]+[verb] 
  


Repeat a same verb once, is called 'redoubling'. A redoubled verb indicates the action happens in a slight degree and a short duration.

Example: 

點頭 ( nod head); 點點頭 ( nod head slightly)

試 (try); 試試 (try a little )

看 (look); 看看 (look briefly)


  
  [verb]+[counting word]+ [ verb] 
  


In the cases of a verb following by a counting word and then the same verb again, the repeated verb is actually a [verb classifier] 

Example: 

點頭 (nod head); 點一點頭 (nod one nod/ nod head once)

試 (try); 試一試 (try one try / try once )

看 (look); 看一看 (look one look / look once )


  
  The particle 了  following a verb indicate 'completion' 
  


Example:

點了一點頭 (nodded one nod/ nodded head once)

試了一試 (tried one try / tried once )

看了一看 (looked one look / looked once  )


  Now come to your question: what [verb]+了+[verb] indicate?


It is similar to point (3) with the counting word omitted.

點了點頭 = 點了(一)點頭

試了試 = 試了(一)試

看了看 = 看了(一)看