This phrase introduces a comment that you make in a medium-sized group of people, like at a meeting or a party. In a situation like this, if you just make a comment without introducing it like this:

Can I have everyone's attention for a moment? Suzanne, good luck in your new home.

...it sounds too small and unimportant. Starting with "I'd just like to say" makes the announcement feel more complete. As another example is, you can say this in a meeting to the people who work for you:

I'd just like to say that you guys did an absolutely phenomenal job.