A (possibly) slightly weaker notion of inaccessibility of a cardinal number than that of an inaccessible cardinal. See comments in that writeup for why we care enough to make up a name.
A cardinal number a is called weakly inaccessible iff:
We replace the demand that a be a strong limit cardinal
with just being a limit cardinal
Like inaccessible cardinals, it is "unknown" (in the sense of both existence and nonexistence being compatible with ZFC) whether "there are" (in the appropriate meta-mathematical sense) any weakly inaccessible cardinals. Any inaccessible cardinal is a weakly inaccessible cardinal; hence the name.