What is a backup battery for?

is an enclosed device that continues to supply AC power output once
power from the power grid is lost. These devices deliver temporary
emergency power.

What is a Battery Backup?

A typical battery backup device comes in a hard plastic case containing
its transformer, power filter circuitry, battery and power inverter.

Batteries provide DC current, which is then run into a power inverter circuit
to produce AC power for powering computers and their monitors.

Each battery backup unit generally has a battery with the capacity to power connected devices for 40 to 60 minutes or longer.

Running a computer on battery backup allows you to save your work
and properly shut down your computer before the battery is fully discharged.
Battery backup units prevent data loss in the event that power is suddenly lost.

Power Filters

Power filters prevent spikes, small surges and "dirty" (unwanted frequency in the power signal) electricity from entering into a device and causing electrical damage.

Most modern battery backup units have a power filter circuit, generally consisting
of a couple of large capacitors.

Surge Protection

Specially designed circuitry inside battery backup devices do not allow
excess voltage to travel into attached devices.

Preventive measures such as fuses break the flow of current before any
excessive voltage can enter into attached devices and cause damage.

One technique is to allow a part of the circuit board to become completely
damaged; this breaks the circuit, which won't allow any voltage to pass further on.

Once a battery backup is damaged by lightning or a surge, dispose of it. Using damaged battery backups could potentially damage any attached devices or pose a fire hazard.

Not all battery backup units contain surge protection circuitry, so you must refer
to the manufacturer for its specifications.

Who Uses Battery Backups

People use battery backups when:

They live in an area of high storm activity;
They live in an area with a lot of surges or black-outs;
Their computer or equipment was an expensive investment;
They rely on their computer for work or their business; and/or
A lot of work can be inputted safely before needing to save the file.

In Conclusion

Battery backups are useful, providing a new level of protection.
Hospitals use them to continue to power life support systems during a catastrophic
event. They save data and even lives.

Source:

JetCafe: Uninterruptible Power Supply (UPS) FAQ

More Information:

PC World: What is a UPS?