If λ is any ordinal, κ is λ-strong means that κ is a cardinal number and there exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ and That is, M agrees with V on an initial segment.
Then κ is strong means that it is λ-strong for all ordinals λ.
If κ is strong or λ-strong for λ ≥ κ+2, then the ultrafilter U witnessing that κ is measurable will be in Vκ+2 and thus in M. So for any α < κ, we have that there exist an ultrafilter U in j(Vκ) − j(Vα), remembering that j(α) = α.
Using the elementary embedding backwards, we get that there is an ultrafilter in Vκ − Vα.
So there are arbitrarily large measurable cardinals below κ which is regular, and thus κ is a limit of κ-many measurable cardinals.