to agree in principle to participate in the production of a movie, based on the script and some kind of financial understanding between the parties. This is an informal agreement, and may be dissolved at will.
An actor is said to “be attached” to a script when they have read it and negotiated some kind of deal parameters through a representative, in exchange for the use of their name as an attachment.
Movie deals are often put together on the strength of their packages. Therefore, elements and their reps are careful about attaching themselves to projects.
It is considered disreputable to claim an element is attached if they are merely considering or complimenting the project. This is why producers will often use phrases like “(actor name) loves it” or “(director’s name) is interested” – because they can’t ethically say the elements are attached.