The Transatlantic accent is a non-rhotic prestige accent of English that was popular among the US upper classes in the first half of the twentieth century, and can be observed in a number of old Hollywood movies. At the time, it was called the “Standard American” or “Eastern Standard” accent (eastern here referring to the US east coast); the modern monikers of “Transatlantic” and “Mid-Atlantic” have been coined because the accent was modelled somewhat on English Received Pronunciation, so to modern listeners it sounds “halfway between” a General American and an RP accent. I prefer the term Transatlantic, because “Mid-Atlantic” is ambiguous (it can also refer to the regional accents of Baltimore and Philadelphia), and in the modern era its “halfwayness” between General American and RP seems exactly what is interesting about it, not its traditional use as the prestige accent of the US east coast elite.
Most of the Transatlantic accent’s vowels, certainly its monophthongs, are similar to those of RP. The big exception is its implementation of the trap-bath split; while the Transatlantic has the trap-bath split, the BATH vowel does not merge with the one of PALM, instead only lowering to /a/, resulting in a three-way distinction between realisations of ⟨a⟩: /æ/ for TRAP, /a/ for BATH, and /ɑː/ for PALM. Other points to note include that the STRUT vowel is always /ɐ/ in Transatlantic (which is a possible realisation in RP too, but RP’s STRUT vowel is more variable) and that the GOAT diphthong is the more American /oʊ/ (in RP it’s fronter at /əʊ/).
Also unlike RP, in most cases a “missing” post-vocalic ⟨r⟩ is not simply dropped, but replaced with schwa. So for example, “car” is /kɑə/ in Transatlantic, and “torn” is /tɔən/. The exceptions would be the NURSE vowel (which is a monophthongal /ɜː~ə:/) and schwa itself, which doesn’t “double”.
The main reason that I personally like the Transatlantic accent, and kind of wish it would make a comeback, is that I find it a crystal-clear “neutral”, “artificial” accent that seems like it could be analoguous to that “neutral Latin American” accent used in movie dubbing in Spanish. The Transatlantic accent seems to try for the absolute minimum number of mergers possible, so pairs/triads like father-bother, cot-caught, Mary-marry-merry, Rosa’s-roses, wine-whine and hurry-furry are all distinct. /t/ and /d/ cannot be flapped or assimilated into a neighbouring consonant (so winner and winter cannot sound the same), yod-dropping is not a thing except after /r/ and optionally /l/ and /s/, and the accent also does not affricate consonants with yods (so for example, “duke” is always [djuːk] and never [dʒuːk]). It just seems that for the purpose of maximum clarity, this would be the accent that English speakers should use. But of course, it was always artificial, and I don’t think it would be desirable to return to the days when ordinary people’s authentic accents were seen as inferior compared to these artificial ones that, naturally, only the elites could afford to learn. It’s not like I think we should use it for everything all the time. Just… maybe more things than zero? 🤣