Primase is unique to DNA replication. Unlike RNA polymerase, which can begin transcribing independently (provided it's at the right location - i.e a TATA box), DNA polymerase needs a little help to get going. To help out DNA polymerase, primase lays down an RNA primer at the beginning. DNA polymerase then latches on to this (at the 3' OH) and continues on its merry way, replicating another DNA molecule.
The RNA primer obviously doesn't match our new DNA strand, however, and so this will eventually be replaced with DNA by a different DNA polymerase.