About your own bookings and events, yes — reminders, a cancellation, a payment recorded or refunded, a nudge to leave a review once a session you were part of is completed, a recap from an event you had a seat at, announcements from communities you belong to, and, for an event you organise, what happens after you publish it: approval, a request for changes, or a takedown. If you offer sessions, also the answer to your request to be listed in Experts and a note if you stop being listed. If you run a community, also how it is doing in its first 30 days. Those are part of the service and you get them because you use it.
Anything else only if you ticked the box. It is not ticked for you, it is not required to use openhour, and you can untick it at any time in your profile, or with Unsubscribe at the foot of any update email — one click, no sign-in.