Spatial memory safety means that a language (at least in its subset that's designated "safe") doesn't allow you to manufacture pointers into memory that may contain data of a different type than what's expected by the pointer (we'll call such pointers "invalid"). The classic examples of spatial memory safety is guaranteeing that arrays are never accessed out of bounds (hence "spatial", as in pointers are safely constrained in the address space). Zig guarantees (except when using delineated "unsafe" code) such spatial safety.

Temporal memory safety is the guarantee that you never access pointers that have been valid at some point in time after they've become invalid due to reallocation of memory; we call such pointers "dangling" (hence "temporal", as in pointers are safely constrained in time). The classic example of this is use-after-free. Zig does not guarantee temporal safety, and you can accidentally have a dangling pointer (i.e. access a one-time valid pointer after it's become invalid).

Invalid pointers are especially dangerous because, in languages where they can occur, they've been a very common source of exploitable security vulnerabilities. However, violating spatial memory bounds is more dangerous, as the result is more easily exploited by attackers in the case of a vulnerability, as it's more predictable.