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