word choice - What is the difference between can and could in 'Can/could you please explain this to me?'

Can you please explain this to me?

Could you please explain this to me?

I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.

What is correct way to use these words?

Answer

The quick answer: In most contexts, these two words are effectively synonyms, especially when discussing possibility, e.g. "(Can/Could) you [perform some action]?".

Longer answer:

There is a somewhat subtle difference in these two phrases that becomes a lot less subtle in different contexts. Let's take the words one at a time:

• 
  
  

  Can deals with actual, literal ability to perform an action. When you ask if someone can explain something, you are literally asking whether they are capable of explaining it. Edit: It is important to note that, as @J.R. has pointed out, this is by no means the only use (or even the most common use) of the word can or the phrase can you .... This construction is often abused to mean effectively the same thing as could you..., i.e. would you be willing to..., etc.

  
  


• 
  

  Could deals with the possibility of performing an action. It is definitely a subtle difference, but basically, when you discuss possibility, you generally are aware of their ability to do it but are tentative about their willingness or availability to perform the action. This is by no means an exact definition.

  
  

It is also worth noting that the word could is actually the past tense of can. In English, using the past tense form of a word in this way is often meant to indicate tentativeness.

I wanted to talk with you.
I wondered if you would be available this afternoon.

I thought it might a good idea.