Refers to demonstrating consistency of results between independent studies. It is one method for guarding against the promotion of false positive results. In relation to MR, genetic variants that are used as instrumental variables (IVs) should be shown to have consistent results across two (or ideally more) independent studies.
Replication has commonly been defined as associations across studies being "statistically significant". This assumes similar statistical power across studies and showing consistency of direction and magnitude of association is also valuable.