Right-to-Left Reading
Japanese manga is read from right to left: the book opens from what an English reader thinks of as the back, and panels run from the top right of each page.
In depth
Japanese is traditionally written in vertical columns from right to left, and manga pages follow the same direction. A manga volume opens on the right; on each page you read the panels starting from the top right, moving left and then down; speech balloons follow the same order.
Flipped and unflipped
Early English editions mirrored the art so it read left to right, which reversed the drawings — characters became left-handed and printed signs ran backwards. In the early 2000s publishers began releasing manga in its original orientation, which was cheaper and faithful to the art, and readers adopted it quickly. Most English manga now carries a page at the "front" reminding readers to start from the other end.
Manhwa and manhua
Korean and modern Chinese comics usually read left to right, like English books.
Translation choices
Keeping the original orientation also preserves sound effects drawn into the art and the composition of double-page spreads, which would be reversed by flipping. Translators adapt only the words inside balloons.
What it means today
For a first-time manga reader: start at the right-hand cover, read each page from the top right, and expect to forget it is unusual after a few pages.