When you see that symbol if you tap that box it means a pop-in menu will slide in from the left edge of the screen.

If you touch the one in the Performance Name box, for example, options concerning the Performance as a whole appear at the left side of the screen: Performance Category Search, Performance Edit, Recall, Performance Property, Favorite.

If you touch that same symbol in the individual Part “Type/Name” box, you will see options for: Part Category Search, Part Edit, Part Copy, Part Delete, (if Part 1 is tapped, Part Property appears in place of Part Delete — you cannot Delete Part 1).

The symbol also appears wherever a list of options is available.
There is usually an “X” to close the options or press [EXIT] after making a selection

Of course!
Thanks for the explanation, it all makes sense.

Now that I know exactly what it means, I think it's a great visual aid in outlining where you could look for options/tweaks.

I didn't manage to find an explanation in the manuals and I think it's very useful to know this.
Could be an useful addition to the Mastering MODX series of articles or to one of the Synth Tips.

Other threads with related answers (and more):
https://www.yamahasynth.com/ask-a-question/what-does-this-menu-icon-mean
https://www.yamahasynth.com/ask-a-question/what-is-this-icon

A tutorial that covers the icon (not the most intuitive to find):
https://www.yamahasynth.com/learn/montage/mastering-montage-montage-user-and-library-files
... look for "The icon in the upper right corner of each box indicates that touching the box will cause a option pop-in box to appear at the left side of the screen." and the following picture.

The key word for that icon is "pop-in". As it mostly is applied to this icon. Although sometimes I see "pop-in" for other menus that appear on the left-hand side but come from from a "v" looking icon.

The "Mastering ... User And Library Files" tutorial is nice in that it explicitly connects the icon to the idea of a left-side "pop-in" menu. Another document "Mastering MODX: The Basics" mentions "pop-in" but does not connect this idea to any icon so there was a missed opportunity to help familiarize the user with icons earlier in the more basic documents. You'll have to read a bit more to find the buried treasures, so to speak.

I watched an interesting video yesterday about Dorico and how much of the interface is "janky" - the narrator's term. He happens to a pro UX/UI designer. The video can illuminate more about this. What resonated so much with me was the idea that a UI doesn't have to be difficult to use while maintaining power. You can have both by making changes that help eliminate the requirement to thumb through documentation, forums, etc. in order to make sense out of a product and how to use it. The video gives specific examples for Dorico - and I think similar approaches can lead to what I've always termed as "elegance" in further improving Yamaha synth design. I think this is much of what a possible role is for ideascale - although it would be nice to have as much internal (Yamaha) team reinforcement of this as possible.

Here's the video - I'm alluding to. It's a good watch: https://www.youtube.com/watch?v=S-3wEC6Fj_8

I highly recommend the many Beginner/Intermediate, and Advanced MONTAGE tutorial articles, which introduce many of the shortcut and navigation options in the context of the features being covered.

A list of the symbols may indeed be impressive, but I find actually navigating through the architecture with a purpose is the best way to learn the language and shortcuts. For example, each of the tutorials on ”MONTAGifying Motif XF” takes you around different areas and provides a variety of ways to get around the architecture.

The tutorial articles are written to be followed while seated at the instrument. Each step reveals an important feature, function or shortcut. The tutorials concerning Super Knob programming introduce important concepts — especially if you are making the button pushes as you go — and often provide several ways to approach it.
Easy enough to find. Search: ”Mastering MONTAGE”
The one on User and Library Files dates back to the original release and should be on your reading list as soon as you begin editing, storing and making your own Files.

The series starts out navigating the “long way” (so you know where you need to go) and slowly we introduce the navigation options and shortcuts/wormholes that make tweaking parameters in two related areas of the architecture much easier (and appreciated)… I have found that learning any piece of gear (like MONTAGE) requires an overview map. This is provided in the MONTAGE through each screen, as you navigate into the architecture, having a name (upper left of each screen). In doing support, you can quickly tell if the questioner has this overview map visualized or not.

I’m found of saying, there is nothing in the screen by accident. Listing all the symbols and studying the list is one way to learn them. I find adding them, like you would words to your vocabulary, is best accomplished in some context.

Don’t try to tackle all of the tutorials at once but if you do them a little at a time, it’s a great way to add them (like Merit Badges) to your workflow. Now that you know what that symbol means you will use if from now on. In fact, you’ll now see it more often.

I highly recommend the many Beginner/Intermediate, and Advanced MONTAGE tutorial articles, which introduce many of the shortcut and navigation options in the context of the features being covered.

Just realised that I put this thread on the Montage section while I am a MODX user.
Anyway, this is what I am doing at the moment, following your Mastering MODX series of tutorials and I have to say it's amazing, thanks for writing it.

A list of the symbols may indeed be impressive, but I find actually navigating through the architecture with a purpose is the best way to learn the language and shortcuts.

Yes, but an explanation of the user interface symbols is meant to help with that.
I mean, those symbols ARE put in the user interface to indicate something to the user. So they should be explained in the manual, in order for the user to be able to use them as intended.
I am that kind of old-school user who actually reads the manuals and tries to understand the basics of the operation of some device / software. I did spend time looking for explanation of some symbols of the GUI.

Looking in the MODX Owner Manual, Page 26 (Performance Play Display) or the Reference Manual page 27, where all the stuff in the Perf Home page is detailed, there absolutely no valid reason for the explanation of this menu symbol to be missing.

What is missing from any of those manuals is one page in the docs, called something like "User interface conventions and symbols", which offers clear explanations (just like the one provided by you above) for the following symbols:

Some of them might be "self explanatory".
Maybe, but that doesn't mean their clear functionality shouldn't be documented. For example, one of those symbols above opens a pop-in menu with various ACTIONS to execute. Another opens a list menu with various ITEMS to choose from. Similar on surface, very different in action.

Hardware buttons like LIVE SET, MASTER VOLUME, SHIFT, ENTER etc are also self explanatory yet they are carefully documented.