In
evolutionary biology these are two terms used by
Richard Dawkins to try to clarify what
kinds of thing are selected by
natural selection, and
how.
They come from his distinction of a replicator as a thing which actually copies itself or gets copied, and a vehicle as a thing that a replicator creates in order to cause and promote its own replication. Normally in biology the replicators are genes, and the vehicles are bodies. Genes code for powerful and efficient bodies, which strive to survive, flourish, and eventually propagate their kind. Their offspring inherit the genes if the genes were for bodies that were good at this.
The question of where natural selection acts in biological evolution is usually phrased in terms of genes and larger vehicles: cells, individual organisms, populations or colonies or kin groups, or species; and perhaps even larger lineages than species over deep time. But doing this may give a false trichotomy: which one is really true, gene selection or organism selection or group selection? The replicator/vehicle distinction is intended to untangle this.
Another reason for the terminology is that things other than genes may be replicators: computer viruses and memes are the two most prominent candidates for treatment similar to the biological; but there are also biological replicators that are not organized as genes and which don't build bodies: so-called selfish DNA.
The replicator is the thing which actually benefits from surviving an environmental test. Genes for running fast appear in lots of little baby bunnies if mummy and daddy bunny kept running fast enough to meet each other and avoid foxes. Whereas the vehicle is the thing which undergoes the environmental test. Genes don't run. Individual rabbits run, escape, get hurt, or get caught.
Vehicle selection is selection on vehicles. Replicator selection is selection for replicators.
But surely rabbits also benefit, not just rabbit genes? Individual rabbits benefit if their genes gave them good legs, and the rabbit species also prospers if good genes are common in its gene pool. Very true. This point is sometimes made against a gene-selectionist view. There is one more distinction I need to add. This relates to the fact that 'evolution' and 'natural selection' are often carelessly confused. Natural selection is the process that happens in a testing environment (climate, predators, rivals etc.). Evolution is the result of that process; or rather, one result.
Yes, rabbit genes and rabbit bodies and rabbit groups all benefit from whatever combination enables them to pass environmental tests: luck, abundant food, good genes, whatever. The difference is that rabbit bodies don't survive. Organisms reproduce but do not replicate. The individual benefits until its death. An advantage that dies with the bearer is no use to its offspring. Any advantage that can be inherited may benefit other survivors, such as offspring. An abundant food source may be heritable until numbers increase to the point where they're using it up. A good nesting site may be won by an individual's strength or cunning and re-used by their successors. But these advantages will last a small number of generations and no more.
The gene however is potentially immortal, passing from body to body, into new populations (whose prosperity it might itself be aiding in), into new species. In the long term - in the evolutionary time scale - selection acting on vehicles does not benefit the vehicles. They are transitory, long gone. Selection acting for replicators is the only process that continues to shape its target (genes) long enough to produce evolutionary effects.
Further reading: Dawkins, The Extended Phenotype.