More correctly called A Girl in Gaea (but I usually see it referred to as "Escaflowne the Movie" or "the Escaflowne Movie") this is, not surprisingly, an anime movie based loosely on the anime series Tenkuu no Escaflowne (Vision of Escaflowne). For those who have seen the series, but not the movie, you may be asking "What's different?" A better question would be "What's the same?" This is because the movie and the series are almost completely unrelated.
For starters, the things that are the same. Mostly, these are characters. Hitomi is still a schoolgirl from Earth who gets transported to the fantasy world of Gaea, whose inhabitants regard her as having some mystical significance. However, she is no longer the rather cheery track star and fortune teller that she was in the series. The movie Hitomi appears to suffer from depression and is contemplating suicide!
The other main character in the movie is Van, who is also significantly changed. Unlike Van in the series, the movie Van is a half-naked badass warrior who cuts through enemy soldiers like they were made of butter.
The movie focuses on these two characters almost to the complete exclusion of all others (a big change from the series, with its intricately entwined plots and subplots. However, most characters from the series make at least some appearance. Allen is present, but is not on camera that much, despite him being a character of nearly equal importance to Van and Hitomi in the series. Folken is rather darker than the series version (which is probably necessary since Dornkirk is thankfully absent). Dilandau is relatively unchanged in terms of characterization (He's still a psychotic, pyromaniac bishonen), but lacks the backstory from the series, being, apparently, a mercenary.
I was pleased to see that Merle(Merulu/Meruru/whatever) got a fair amount of screen-time, as she was probably my favorite character. (Incidentally, while her new character design is a general improvement, i.e. no more shoulder pom-poms, I was very disappointed to see that she wore panties. Catgirls should not wear underwear). Another character who was surprisingly prominant was the moleman, who acted a priest and diviner.
As far as the setting goes, Gaea is still a world, invisible from Earth, in which both Earth and the Moon are visible, and still has a steampunk/fantasy feel to it. However, the nations have changed completely. Zaibach, the Evil Empire from the series, is replaced by Folken's Black Dragon Clan who nevertheless wield a similar style of technology. Interestingly, they seem to be about the only users of airships (unlike in the series, where such vessels were common). Even the heroes no longer travel in an airship, but rather in a truly massive wagon. Also, the Guymelefs that made up such an imporant part of the armies in the series are absent, save for two (one of which is Escaflowne itself). Both are ancient relics, and both have a more biological, Evangelion-like feel to them. The general appearance of the armors is similar to their equivalents in the series though.
The music, of course, is excellent. It is, once again, composed by the incomparable Yoko Kanno, and lives up to the high standards I've grown accustomed to in her work.
In all, this is a worthwhile movie to see. I don't believe it is out on DVD or VHS yet (I saw it at Anime Expo) but when it does come out, it's worth at least a rental. I'll probably buy the DVD. It really works best if you go into it not expecting a remake of the series, because the stories really are completely different, despite having similarly-named (and similar-looking) characters and similar mecha designs. Both movie and series excel in the limitations of their own respective media, and both are worthy of watching.