As a rule, everything around you glows – in other words, it emits photons. Some infrared ones, some visible ones, some ultraviolet (or even higher-frequency) ones. How much of each depends on the temperature of the material. Most things (e.g. you) are too cold to be visibly glowing, but they still emit plenty of infrared radiation.
Now, standard solar cells convert visible photons into electricity. Any incoming infrared photons, however, aren't strong enough to kick any electrons loose, so they go to waste. Here, the researchers used carbon nanotubes to absorb the wasted infrared photons. This heats up the nanotubes, which then emit visible photons, which then increase electricity generation.
There is no way to convert heat to electricity directly, unfortunately. However, you can get small amounts of electricity out of temperature differences: https://en.wikipedia.org/wiki/Thermoelectric_effect