Bacteria as predators
They do that because a bacterium contains all the molecules required for life, that is they are a source of amino acids, lipids, glucids and nucleic acids. This is the same reason why we eat in the first place: we need a source of these molecules to survive or, in other words, to allow our cells to carry out their tasks such as replicating the DNA or producing proteins. 

Bacteria can kill other bacteria by a kind of infection: the predator bacterium enters a bigger prey and then start consuming the prey's molecules. By the same token, Mycobacterium tuberculosis enters the macrophages and used them for its own biochemistry, for instance. 

Interestingly, this process of bacterial predation is under scrutiny for the development of a new breed of antiseptics in the age of antibiotic resistance (see https://phys.org/news/2017-03-predatory-bacteria-antibiotic.html).