Meaning of “running” - Learner’s Dictionary

running

adjective uk us /ˈrʌnɪŋ/

[ always before noun ] continuing for a long time:

a running battle
a running joke
second/third, etc day/week, etc running

B2 If something happens for the second/third, etc day/week, etc running, it happens on that number of regular occasions without changing:

He's won the Championship for the fifth year running.
running water

If a place has running water, it has a working water system:

They bought an old house with no electricity or running water.

(Definition of “running adjective” from the Cambridge Learner’s Dictionary © Cambridge University Press)