What type of organism appeared during the Ordovician Period?

The first true vertebrates evolved about this time.

The first vertebrates (our ancestors) evolved during the Ordovician period. This time period is also known as the first time arthropods (insects) and plants probably colonized the land - for the first 3.5 billion years or so of life's evolution, marine environments were the sole place where life thrived.

http://www.ucmp.berkeley.edu/ordovician/ordovician.php

The end of the Ordovician is marked by a mass extinction event that killed off many marine organisms. This was probably brought on by a massive volcanic eruption that pumped huge amounts of CO2 into and in so doing, tripped off a global warming event.