Simply stated, let's say you have an LED that needs 3.7 volts to run at it's brightest. If you use 2 AA batteries, they'd give 3 volts DC. A DC-DC converter would bring that up to the ideal 3.7 volts. As the batteries faded below 3 volts, the converter would correspondingly fall below 3.7 volts. On the other hand the more complicated "regulated" converter, would keep it at the 3.7 volts till the batteries went below a certain threshold.
Another example would be 1 AA at 1.5 volts that would be boosted to 3.7 volts by a "more powerful" DC-DC converter.
DC cannot be converted to a higher voltage directly. You have to change to AC first, convert, then change back to DC. This is accomplished by an oscillator circuit in the DC-DC converter that changes the DC to AC, and a rectifier (diode) that changes it back to DC.
Sounds complicated, and it is, but can be done in a very small package. Obviously some circuits do this better than others, giving better efficiency.