The period starts from the first wipe after one’s wudu’ is invalidated. When a person puts on socks while being in a state of purity, and thereafter he becomes impure (by defecating for example), then he may wipe over the socks when performing al-wudu’. This would be considered the first time he wiped after putting on the socks. From this time the period of a day and a night (24 hours) starts to be counted. For example, A man performs wudu’ by washing his feet, and thereafter puts on his socks and prays fajr. His wudu’ was invalidated around 10am, and then he performed wudu’ around 11am to observe the mid-day optional prayer (Salatudh-duha), wiping his socks in the process. From this time onward, he is permitted to keep on wiping over his socks until 11am of the following day. This is for the non-traveller. As for the traveller, however, it (the wiping period) is three days and three nights.
What Invalidates Wiping

1- Termination of the prescribed period of wiping.
2- Removal of one or both of the socks.
3- Occurrence of greater impurity. Safwa’n Ibn ‘Assaal t said: “The Prophet ﷺ used to order us, when we were traveling, not to remove our leather footwear (khuff) for three days and nights, except for Janabah (sexual discharge). That is do not remove them for defecating, urinating, and sleep.” [ narrated by At-Tirmidhi.]
source: Wiping over socks, casts, and bandages for wudu (ablution)