Each spellcasting class has a Spellcasting Focus section under Spellcasting heading which indicates what type of focus can be used by that class. For example, a Bard can use a musical instrument (PHB 53), a Cleric can use a holy symbol (PHB 58), and a Druid can use a druidic focus (PHB 66).
Chapter 5 lists the costs of various spellcasting foci (PHB 150) under Arcane focus, Druidic focus, Holy symbol, etc. There are also a brief descriptions on the page following the list (PHB 151).
The Material section under the Components heading of Chapter 10 (PHB 203) indicates that a spellcasting focus can be used in place of material components for a spell if there is no cost indicated in the spell description and the material components are not consumed.