Wi-Fi extenders work by creating access points to extend your Wi-Fi signal into areas that are either out of range or being blocked due to materials within your building or frequency interference. Extenders come in the form of repeaters that boost the signal using antennae and access points that require connection to computers via Ethernet cables.
In addition to building materials, a Wi-Fi signal may be blocked by devices using similar frequencies as its router. These devices include both cordless phones and microwave ovens.
A repeater works by boosting the signal using antennae and has the benefit of not requiring a physical connection to the computer. It must simply be placed within range of the existing network, and it then extends that by using its own broadcasting capabilities.
The access points work by connecting to the computer via an Ethernet cable and then broadcasting a signal in a similar manner to the router. This method of boosting Wi-Fi is more suited to homes or workplaces that are already set up as physical networks, because it can be used to selectively boost the signal at less cost than boosting the signal via repeaters.
It is important to verify that a repeater is able to broadcast on the same wireless frequency that the home or work network uses.