For us earthlings, anyway, interstellar travel is still confined to fiction. So we can assume we are talking about something metaphorical.
Ad astra is a Latin phrase meaning "to the stars". The phrase has origins with Virgil, who wrote:
- sic itur ad astra ("thus one journeys to the stars", from Aeneid book IX, line 641, spoken by Apollo to Aeneas's young son Iulus) and
- opta ardua pennis astra sequi ("desire to pursue the high (or hard to reach) stars on wings" book XII, lines 892–893, spoken by Aeneas to his foe Turnus in their combat).
Another origin is Seneca the Younger, who wrote:
- non est ad astra mollis e terris via ("there is no easy way from the earth to the stars", Hercules Furens, line 437, spoken by Megara, Hercules' wife).
So the phrase "to the stars" simply invokes an inspirational notion of accomplishing some hard-to-reach goal.
The Wikipedia article goes on to say that the phrase is used "as, or as part of, the motto of many organizations." For example:
- Quam celerrime ad astra ("Speedily to the stars") is the motto of the Chilean Air Force.
- Sic itur ad astra ("Thus one goes to the stars") is the motto of The Geelong College in Australia and the Alice Smith School, Kuala Lumpur, Malaysia.
- Per ardua ad astra ("Through struggle to the stars") is the motto of Stevens Institute of Technology in Hoboken, New Jersey as well as the city of Gouda in the Netherlands.
In the context of a toast, it would probably mean that the person is wishing someone well in their life's goals and their journey to meet them. As for "to the stars and beyond with someone," I'd interpret that to mean the two people are embarking on some journey together (it could be marriage, it could be a business venture), and the person is wishing them success.