I often make and receive phone calls in a business context where the other person talks with too much jargon. Occasionally I need to interrupt them with questions to get a better understanding of what they are saying. How can I go about politely interrupting them for clarification without offending them?
If people just continue talking and they don't pause just say:
And then tell them that you like to understand them but you didn't understand this or that and could they please repeat this (and maybe explain it with other words).
I think the important part is that you should tell the person that you want to understand them but are not able to understand them. Most people want that others understand them. There is no point in talking and talking when the other(s) don't understand it.
If you just continue to "listen" without understanding then maybe the other person talks for 5 minutes and you understand little because you didn't understand the beginning. If you tell the person then something like "sorry, I didn't understand what you said 5 minutes ago" then it is a lot more likely that the other person is upset and maybe ask you: Why didn't you ask me 5 minutes ago?
That is my personal experience as listener and, I have to admit, also sometimes as the person who talks and has to be interrupted. I was never angry with anybody who interrupted me (maybe after 15 seconds) because they didn't understand me. I get angry when people interrupt me already after 5 seconds because they don't want to listen but that is a different issue.
55% of communication is body language this makes it much more difficult to communicate with people over the phone and sometimes you need to resort to doing unnatural things.
Wait for them to finish and just explain your problem to them
I couldn't understand some of the jargon you were using but I was afraid to interrupt and offend you let's agree that I will do that in the future and you wont get offended.
Say the last part jokingly and add a chuckle in the end if you feel like it.
This is a very, very common scenario. So don't worry too much about how you come across.
So long as you use normal pleasantries (Excuse me, can we, etc.) you're all good. Meaning, don't be rude or obnoxious, that's your Manager's job if it comes to it.
Them: By using the Snodgrass technique, we can overcome the Flingminders…
You: Excuse me a sec, hey, can we go back a bit. Can you give background on Snodgrass?
Here's the thing, you can't worry too much about how they might feel, you need the information and interrupting them is the only way to get that. You will find that occasionally, you will need to get more assertive in the interruption, but again, do what you have to do.