How does Victor Stone gain new abilities?

As Valorum noted in his comment, Victor has the technology of an Apokoliptan Mother Box integrated into his physiology. It is not explicitly spelled out in the film, but it's implied that the box integrated with the cybernetics Silas had implanted in him to save his life after the car accident, with his system partially being under Victor's control and partly being co-opted by the Mother Box to further its purpose, whatever that is. Thus, one of Victor's prime complaints in the film is that he is becoming more alien and more machine as the Mother Box transforms him, with one of his fears being that the transformation will remove the part of him that is human, and Victor Stone, leaving just the machine.