Transduction is the process in which DNA is moved from one bacterium to another. When bacteriophages (viruses that infect bacteria) infect a bacterial cell, their normal mode of reproduction is to harness the DNA replication machinery of the host bacterial cell and make numerous copies of their own DNA. These copies of bacteriophage DNA are then packaged into newly synthesized copies of bacteriophage virions.
However, the packaging of bacteriophage DNA is not fool-proof and at some low frequency, small pieces of bacterial DNA will be packaged into a bacteriophage virion instead of the bacteriophage genome.
Upon lysis of the host cell, the mispackaged virions containing bacterial DNA can infect other bacterial cells, thus transferring bacterial DNA from one cell to another.
More generally, transduction is the process by which genetic material, e.g. DNA or siRNA, is inserted into a cell. Common techniques in molecular biology are the use of viral vectors (including bacteriophages), electroporation, or chemical reagents that increase cell permeability. Transfection is a more common term, although transfection sometimes implies expression of the genetic material as well.
Alternatively, transduction can be shorthand for Signal transduction.