There are four main quest types in Witcher 3. Each quest category has its own tab in the journal. Those categories are:
Main quests - All these quests Geralt receives automatically and they must be completed in order to move the storyline forward. Most main quests have specific requirements, but some of them require you to complete various other tasks. Often you can choose the order in which you will complete the main quests you receive. But keep in mind that the order you choose might have an impact on future quests. For example, if you first play the quest A, the quest B might be different than if you would have chosen it as the first. And if you start with quest B, then quest A might be different.
Side quests - All these quests are optional. You will learn about them from notice boards or by finding the quest givers on your own (exclamation marks on the world map). There is a great variety to them. Some are short, easy and offer small rewards, but there are some longer, more demanding quests as well that offer great items for completing them.
Witcher contracts - A special category of side quests. Just as standard side quests, you can unlock contracts by checking the notice board or by finding the quest giver. You should visit the quest giver before going for a hunt anyway and bargain better reward for completing the task. All quests from this category are about finding and killing strong monsters. Always check the suggested character level and don't try to complete contracts too early because you might be too weak for that. You should prepare before the battle as well (oils, bombs, signs etc.)
Treasure hunt quests - Another specific form of side quests. Your task is to find the places in which you can loot a treasure with valuable diagrams, weapons or armor parts. You can activate and add to journal quests from this group in two ways. First is examining the location with hidden treasure on the world map (one of the optional locations type hidden under a question mark). Usually you will find some letter or other document linked to the quest. Second way is finding one of the treasures directly, without the notes that guide you to it. Important - some quests from this group are larger and consist of few parts, allowing you to collect, for example, rare parts of witcher gear.