"Managed" is a pretty general term. In the context of DX9, it means that a copy of the texture will be kept in system RAM, and reuploaded to the GPU whenever a lost device event occurs. This can happen if you change resolutions, alt-tab, minimise, etc.
The other option would be "Default", which means that only a copy is kept in video RAM. When a lost device event occurs, and you don't have the texture in system RAM, it means the game will have to reload all textures from disk.
I'm assuming that the game is letting you save some system RAM in exchange for excruciatingly slow (or non-functional) alt-tab. It can be a concern if it's a 32-bit executable and you're hitting the 2GB limit.