What does it mean if we disable K-rule in Agda?
Axiom K is related to "Uniqueness of Identity Proofs", which says is that any two proofs of equality are themselves equal to each other (i.e. are both Refl). Agda doesn't include K as an axiom, but it (and UIP) can be proved as a theorem using Agda's dependent pattern matching.

Axiom K is inconsistent with homotopy type theory, where the univalence axiom provides ways of constructing equalities other than refl. For example, if there are two functions that are pointwise equal, univalence asserts that there is an equality term equating them, but it cannot be refl if the functions have different implementations.

All removing K from Agda does is add restrictions to pattern matching, making fewer matches typecheck. The runtime semantics are unchanged, and no new programs typecheck.

For some excellent introductions on the subject, I recommend:

Pattern Matching without K

Unifiers as Equivalences

Both of these have more detailed versions in JFP if you have access to a subscription.