similar structures are : a week's worth of sth , a month 's worth of sth, a day 's worth of sth ,or a year's worth of sth , meaning an amount of sth that lasts a week , a month , a day , or a year. for example, I always eat twenty apples in a week, so you must give me twenty apples , because these twenty apples will last a week for me. that amount is my week 's worth of apples , that is to say, a week 's worth of 20 apples will last a week for me , if you give me 19 apples , that amount will not last a week to me. so , in the same way you would understand the " a day 's worth of water " , if you usually drink five cups of water a day (each day), then, a day 's worth of five cups of water is the amount of your water , such amount of water will last a day for you to drink. though I am chinese , I think now you would understand . hope this is helpful to you.

'a day' an another new life

It could mean a days worth of work or earnings.

It refers to the amount of something that is necessary, or that can me done/consumed/made in one day (approximation). For example: If you/a family eats 2 loaves or bread a day and 1 litre of milk a week, then one can easily say: We have a day's worth of bread and a week's worth of milk left. i.e: Enough bread for a day... and enough milk for 1 week

Can you give the complete sentence in which this phrase was used? That will help for me to answer your question.