In legal terms, abandoned property refers to any property which has been left untouched by its owner for prolonged periods of time without a clear intention to retrieve it at some later point. The term is a rather broad one, though in the same time there are various restrictions over what can be considered abandoned property, as opposed to misplaced or lost one. Generally, the property must be left in a place where its owner may have intended to leave it - for example, a car parked in the street as opposed to a concealed place away from the road (which would imply theft).
What one can do upon finding abandoned property depends entirely on their local jurisdiction - in most cases, the person who finds abandoned property is legally entitled to becoming its new owner, though there are exceptions to this rule depending on the particular type of property involved - for example, the rule does not apply to vehicles, such as cars and sea vessels. In those cases, the government takes action to remove the property from its location and take it in as state-owned property.
If the owner of the abandoned property can be contacted, they're usually warned that their property has been marked as abandoned and is about to be taken in by the government, though not always directly - for example, in some jurisdictions government officials would simply leave a note on a car instead of calling its owner personally, which has lead to some controversy due to the questionable nature of this practice. Owners are commonly allowed to reclaim their property after it has been taken by the government, often with additional costs attached to it.