A bacteriophage is a virus that infects bacteria. Also called 'phage' for short.
The name comes from the fact that if you have a petri dish with a coating of bacteria, the virus will make little clear circles where the bacteria have died. It looks like something is eating the bacteria, therefore bacteriophage.
Some baceriophage look really neat. For instance, the T4 bacteriophage looks a bit like an alien spacecraft. The majority of the DNA is housed in a dodecahedral 'head', which is mounted on a stalk. Around the stalk are 'legs' that are important in the attachment of the virus to the bacteria. When infection takes place, the T4 bacteriophage positions itself with the stalk pointing towards the bacteria. Then, the DNA housed in the 'head' get's injected into the bacteria. There, the viral DNA subverts the regular function of the bacteria, and makes viral proteins. This leads to the production of new viral DNA and protein, which gets assembled into more alien spaceship-looking bacteriophage, which goes on to infect more bacteria.
Not to be confused with macrophage. And no matter what they say on Star Trek, only bacteria get infected by phage.