The Elibe Series is an unofficial term referring to a grouping of related Fire Emblem games, namely Fire Emblem: The Binding Blade, and Fire Emblem: The Blazing Blade. Both games take place on the continent of Elibe and were released for the Game Boy Advance. However, even though The Binding Blade was released almost one and a half years before The Blazing Blade, it serves as a sequel in terms of plot; the events of The Binding Blade take place 20 years after The Blazing Blade. Several characters seen as children or otherwise in The Blazing Blade appear older in The Binding Blade.
The Elibe Series marked a notable turning point for the Fire Emblem series: the creator and longtime supporter of the series, Shouzou Kaga, left in pursuit of other projects, and the series debuted on a portable console for the first time.
Both games were developed and released for the Game Boy Advance, but The Blazing Blade was the first game in the series to be released outside of Japan (which was simply named Fire Emblem to present the series in other regions). This happened almost exclusively due to the overwhelming popularity of Roy's (along with Marth's) cameo in an earlier released, non-series fighting game, Super Smash Bros. Melee on the Nintendo GameCube.
The Binding Blade was never released outside of Japan, despite its successor's worldwide popularity, a preclusion that baffled many Fire Emblem fans. This was because, while Nintendo of America was willing to localize The Binding Blade, the workload of localizing The Sacred Stones meant that the idea needed to be scrapped, leaving The Binding Blade exclusive to Japan.
As a result, while the Elibe setting is of somewhat average popularity in Japan, it and its characters, particularly the The Blazing Blade cast, tend to be the favorite of many overseas Fire Emblem fans. It is suspected that, while Roy was in Melee mostly for promotional purposes, Lyn made an appearance as a "battle item" in Super Smash Bros. Brawl, in large part due to that character's overwhelming popularity overseas as well. American-produced fan games, such as Elibian Nights or Immortal Sword, tend to focus on this setting.
While some fans of the series include Fire Emblem: The Sacred Stones (the third of the 3 Game Boy Advance titles) as part of the Elibe Series, no hard evidence has surfaced that would suggest that it is linked by setting to the previous two.