"Running out of water" generally means that on a given day, or perhaps for a longer stretch (days, weeks, months) there is not enough water for essential needs, especially sewage, washing, and drinking, but also industrial and recreational activities.
After air itself, water is the most-used substance by humans (followed by gravel, sand, and rock -- we aren't out of the stone age yet), and the quantities and quality (purity) used are great enough that simple stockpiling does not generally work.
Chennai particularly is in the north-eastern monsoon belt with a wet-and-dry tropical climate (Köppen). Monthly rainfall averages vary by a factor of 100, from as low as 3mm per month in the dry season (Jan-May) to over 400mm in the wet (Jul-Dec, especially Oct-Dec). The climate chart at Wikipedia shows this:
https://en.wikipedia.org/wiki/Chennai
There are no rivers. The water table sits at 2m depth typically. And yes, it is recharged by the monsoon. The shortages are critical, but temporary.
With such an all-or-nothing weather cycle, the need is to both shed and drainnwater during the monsoon and to retain it during the dry season. That's a difficult order.
Current forecast is for rain every day.
