Placemarking is sometimes used to mark where you've got to when you want to come back later, especially on a fast-moving 'story' thread, but more often it's so that you can come back later to read it properly, using the 'Threads I'm On' tool. Theoretically you could use 'Threads I'm Watching' for this job, but a lot of us use that to save threads we might need in the future. Mine's got vegetarian recipes and travel advice for places we're planning on going in the next year or two, for example, and I stashed a thread with a lot of helpful info about first periods in there about four years ago, which came in very handy about three months ago.
Not sure if you can 'save' your place on the phone version, since you need to hover over the lower right corner of a post with a mouse to do it, you probably can't.
Placemarking's also used to contribute to threads which look like they're turning into a bunfight/might have been started by a troll etc, and might get deleted, just so that you'll get to see the thread deletion message <admits to having done that once but it was awfully late at night and had had rather a lot of > That's MNHQ's own fault though, for sometimes doing very funny deletion messages!