I don't have expertise in this area, but here's the extent of what I've been able to find about it.
The main distinction that you'll be looking for is between 謙譲語 and 丁重語. Both serve to elevate the listener, and they overlap quite a bit. The key, however, is that the main use of 謙譲語 shows respect to those who appear in the conversation while 丁重語 expresses direct respect to the listener. This use is basically a subset of normal humble speech.
So for example, let's say you're talking to your boss. I'm borrowing these example sentences from the source below:
In the first one you are expressing respect for your boss through using ご説明 with him/her explicitly in the conversation. In the second one you are using 説明いたす to show respect to the listener, in this case still your boss.
To make it a little clearer you can switch 部長 to your friend 山田. He is the same rank as you and therefore doesn't take formal speech. So we take the following examples:
In this situation, 1 is incorrect because you are using ご説明 to show respect to 山田 who is of the same rank as you. 2 is ok because you are not elevating 山田 with ご説明 but you are elevating your boss (whom you are speaking to) by using 説明いたす. This is 丁重語.
And you can take it one step further. You're talking to your 部長 about your 課長. What happens then?
In this case 1 is not necessarily wrong because you are using ご説明 to refer to 課長. You just have to be careful not to upset your 部長 by using formal speech for 課長 but not for him (that is, using 謙譲語 but not 丁重語). 2 solves that by incorporating both forms.
All examples were borrowed from here: