Sucking CO2 out of the air. Burning hydrocarbons (i.e. compounds containing hydrogen AND carbon atoms) produces the greenhouse gas carbon dioxide. This would use energy to suck CO2 out of the air and produce hydrocarbons. The energy stored in those hydrocarbons could then potentially be released again by burning them (which would again produce CO2).
Contrary to the suggestion of the article, they will NOT be able to store more energy for potential release by burning the fuel than they put into creating the fuel from the CO2 in the air. If that were possible, then they have created a perpetual motion machine. I see no reason to believe they can do this.