a “vehicle” that provides a “backbone” for sticking a piece of genetic information (transgene or “insert”) that you want in cells that you want. A few common types are plasmids, viral vectors, & artificial chromosomes. Vectors can differ in how much DNA they can hold, how they get into cells, etc. but they have some things in common including: an origin of replication (a start point for DNA polymerase to make copies of it before the cell divides so the vector gets passed on); a promoter in front of the gene you want expressed (a start point for RNA polymerase to make mRNA copies of it for the ribosomes to make proteins from); and a selectable marker (such as an antibiotic resistance gene) so you can select for cells that have the vector inside.
The whole “vehicle” concept is similar to how mosquitoes can serve as vectors for transporting malaria virus into humans, except when we talk about vectors in biochemistry we’re typically talking about recombinant DNA (DNA in which we’ve inserted a gene or genes of interest, such as the gene for making a protein we want to study). So, if we’re using a viral vector (like an adenoviral vector) we insert a gene into the (weakened) viral DNA and then the virus infects those cells and brings in the DNA we want. Viral vectors are frequently used to get genes into whole animals and can be replicating or non-replicating. It’s easier to get genes into cells in a dish or tube than in the body, so in the lab we often use non-viral vectors, such as circular pieces of DNA called plasmids. These plasmids originally come from a virus that infects bacteria (a bacteriaphage or “phage”) but we’ve “recombined” that phage DNA with the gene we want and we work with the plasmid as “naked DNA” without the phage coat and stuff. By itself, this plasmid can’t get into cells, but we can use “transformation” and “transfection” methods such as heat shock, electroporation, and cationic carriers to get the DNA in.
Most vectors are specialized for cells from a specific organism (such as E. coli or Sf9 insect cells) so they only have promoters and origins of replication that will work in that cell type. But there are also “shuttle vectors” that have the sequences for multiple cell types. So, for example, the bacmids I use to express protein in Sf9 cells can replicate in both E. coli and Sf9. These are useful because it’s much easier to manipulate DNA in bacteria but Sf9 are great for expressing proteins.