1. It's a fuse just like the one in a power cord but much smaller and embeddd into an IC. They are links which can be 'burned out' just like a conventional fuse which means they can't be reset afterwards. They are not used to protect circuitry though, they are used to configure it in a way that can't be reversed. For example, they could be used to permanently store a serial number inside an IC or in some cases, change the way it operates. Another example: some devices fail tests after manufacture becasue one or more sections do not meet specification, in these the faulty section could be disabled and the IC rebranded as a part without that feature.
2. Very little, except maybe as mentioned in 1. There are PROMs (note: not erasable) which are made from am array of fuses which are similar in the way they work.
3. eFuse isn't a program so no, it can't.
Brian.