An UNINTERRUPTABLE POWER SUPPLY (UPS) is a device for filtering power taken in from mains current and storing it. Various devices which do not react well to power failures are then plugged into the UPS. When the mains power goes off, the device provides power from its own storage to make up for the lack. The amount of current and the runtime provided varies from model to model.
There are two systems which fulfill this function: A UPS, or uninterruptable power supply, in which devices on the load side of the system are always running on battery power (or from other energy storage), which is constantly being recharged; And the Standby Power Supply, or SPS, in which devices normally run off of the mains supply, but switch to the backup stored power rapidly enough to not suffer a loss of power. UPS is used as a blanket term to describe all backup power systems.
The advantage of an SPS over a UPS is that the batteries see less use, and therefore are subjected to less heat, and experience longer life. A UPS, on the other hand, provides superior power filtering, and some particularly sensitive devices might not appreciate the switch from mains current to battery power provided by an SPS. SPSes are of course less expensive than true UPSes.
Many, if not most UPS systems provide some level of monitoring, typically via USB (for newer units) or RS-232 serial connection. It may be as simple as alerting the computer that the UPS has switched to backup power, or it might inform the computer how much runtime is left at the current draw. This allows software which will perform tasks such as shutting down delicate or non-essential systems, either to prevent data loss, or increase run time.
The most popular manufacturer of battery backup systems is American Power Conversion, or APC. They make everything from non-power-storing surge suppressors up to site-installed devices providing enough power for entire data centers. Larger devices plug into 220VAC rather than standard 110, and may provide 110, 220, or both.
While UPSes and SPSes generally use Sealed Lead-Acid (or SLA) batteries to store power, companies are now looking to flywheels to store energy. Active Power, Inc. has a system in which the flywheel is in a chamber "filled" with vacuum, dramatically reducing friction. Unfortunately, flywheels and batteries alike have short service lives of 5-10 years maximum. However, the technology of both batteries and flywheels is improving. Companies are also looking into super capacitors, as they have a very high energy density, though they are also extremely expensive.
Another possiblity for the future is to use hydrogen-based fuel cells - One can apply electricity to split air or water into its constituent components, storing the hydrogen, and putting it back into the fuel cell later when power is needed. Such a device would require a great deal of energy to store the hydrogen to begin with, but would result in high power output and long runtimes. You can also burn the hydrogen in a generator, which implies more physical maintenance, but which may actually be a cleaner source of power over time as the result of burning hydrogen is water and heat, while fuel cells are usually made with expensive metals and must undergo a recycling process at the end of their service life.
UPS systems are available in sizes ranging from about 200vA up to whatever you are willing to pay for. They use batteries of all types, and flywheels to store power, and release it when you need it. Some UPSes are expandable, with the ability to add additional cells to increase run time. You can get a small 400vA UPS built into an outlet strip, or get huge modular power systems which take up more room than a refrigerator - Or indeed fill the entire room. In fact, your local phone company probably still has a room full of batteries providing 48VDC to power the POTS phones in your community.