A list with all current items sorted in different categories (like type, tier or the stats they provide) can be found here: List of items.
Consumables are one-time use items that are removed after they are activated. Each god can only carry two different consumables at a time, but most allow of players to carry multiple quantities of each one. Wards and Sentry Wards are an exception to this as players can only carry two wards and one sentry ward at any time.
Chalices are early game consumables that allow players to invest an initially large amount of Gold for a stack of Potions or Wards that can be refilled by returning to base. However, selling these yields no Gold if the player leaves their fountain or spends any charges.
Relics grant the player new abilities like becoming invulnerable for a short duration or reducing the healing received by nearby enemies. Relics must be activated for them to have an effect. Once used they will go onto cooldown before they can be used again. Relics are free, but players can only have two Relics at a time. The first Relic slot is unlocked at level 1, and the second Relic slot is unlocked at level 12. After acquiring one, it cannot be removed from the player's inventory if they have left the fountain or used the Relic. Relics can be upgraded with 500 gold, increasing their potency. The increased effect is usually noted on the upgraded version in yellow.
Passive items are the most prevalent. Each one provides a bonus to one or more stats like Health, Movement Speed, or Magical Protection. Each god can only hold up to six different passive items. Most Tier III Passive items also provide a unique Passive effect, like auras or "on basic hit" effects. There are also a few Tier II items that provide unique effects. While most Passive items can be acquired by anyone, there are a number of items that are restricted to gods with a certain type of power (Physical or Magical); these are mostly the ones that provide Power, Lifesteal or Penetration bonuses. Players can usually carry more than one Passive item from the same item tree, but they can't acquire two of the exact same item or a lower-tier item if all of its upgrades are unavailable. There are some item trees where two items within the same tree cannot be purchased, although this is uncommon.
Passive items are classified in different categories: Starter, Offensive, Defensive and Utility. Starter items are items with a single tier whose bonuses and unique passive effects are most useful on the early stages of a match but gradually become less useful as time goes by. Offensive items provide boosts to stats related to attack and damage output (Physical & Magical Power, Attack Speed, Critical Strike Chance, etc.). Defensive items provide bonuses to stats related to defense and self-preservation (Physical & Magical Protection, Health and HP5). Utility items provide boosts for miscellaneous stats (Cooldown Reduction, MP5, Movement Speed, etc.) or provide supportive and team beneficial bonuses (like Aura effects).