Hearing first but understanding later? I have experienced this phenomenon several times and checked with other people as well.

It goes like this: you hear something, but it's just a sound with no meaning. Some seconds later, you consciously remember the sound and make sense out of it (like a word or a phrase that somebody tells).

Although both processes (remembrance and understanding) are fairly common, I find it weird that understanding is not automatically triggered when processing a sound and it can be demanded on purpose

Is there any name for this phenomenon? (Would appreciate some detail on it too.)
The phenomena broadly makes sense in terms of information processing models of memory and cognition.

The phonological loop

For example, you could think about the phenomena in terms of a phonological loop. To Quote the Wikipedia article on Baddeley's model of working memory


  The phonological loop (or "articulatory loop") as a whole deals with
  sound or phonological information. It consists of two parts: a
  short-term phonological store with auditory memory traces that are
  subject to rapid decay and an articulatory rehearsal component
  (sometimes called the articulatory loop) that can revive the memory
  traces.
  
  Any auditory verbal information is assumed to enter automatically into
  the phonological store. Visually presented language can be transformed
  into phonological code by silent articulation and thereby be encoded
  into the phonological store. This transformation is facilitated by the
  articulatory control process. The phonological store acts as an 'inner
  ear', remembering speech sounds in their temporal order, whilst the
  articulatory process acts as an 'inner voice' and repeats the series
  of words (or other speech elements) on a loop to prevent them from
  decaying. The phonological loop may play a key role in the acquisition
  of vocabulary, particularly in the early childhood years.[3] It may
  also be vital for learning a second language.


Applying this to the phenomena


In the very short term (perhaps a few seconds), you presumably have a internal representation of the raw sound, which might if you were to attend to it afterwards be then processed into words and meaning.
Alternatively, you may hear the words but not process the meaning. Presumably these words can remain represented for a little longer in your short term memory than can the raw sounds (as a very rough guess, perhaps up to 10 or 20 seconds). And then you can return to the words and process them.
Another possibility is that you have basically processed the meaning of the original words, but were perhaps immediately distracted, and then a little later you remembered what was said and that you need to respond.