“Hashavas aveidah” is the mitzvah to return a lost object. The reason for this mitzvah is simple enough: it’s fairly common for people to lose things. It is therefore a benefit to society to encourage people to get as many lost objects back into their rightful owners’ hands as possible.
Of course, some lost objects are easier to return than others. If you find a wallet, a camera or a cell phone in the street, it’s more likely that you’ll be able to identify the rightful owner than if you find a fifty-dollar bill. The Torah only requires us to return things that have identifying characteristics. Loose money, for example (as opposed to in a wallet or purse), has no identifying traits and its original owner need not be sought.
Other factors coming into play in the laws of lost objects include whether the item was found on private or public property, whether things were scattered or neatly stacked, and whether the finder incurs an expense by guarding the property until the owner can be identified (such as feeding a lost dog).
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Baba Metzia starting on page 21a and codified in the Mishneh Torah in the eleventh chapter of Hilchos Gezeilah. This mitzvah is #204 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #69 of the 77 positive mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.