Durations
Source Player Core pg. 300
The duration of a spell is how long the spell effect lasts. Spells that last for more than an instant have a Duration entry. A spell might last until the start or end of a turn, for some number of rounds, for minutes, or even longer. If a spell's duration is given in rounds, the number of rounds remaining decreases by 1 at the start of each of the spellcaster's turns, ending when the duration reaches 0.
Some spells have effects that remain even after the spell's magic is gone. Any ongoing effect that isn't part of the spell's duration entry isn't magical. For instance, a spell such as sunburst that creates a brief, intensely bright flash of light might blind someone for a time, even permanently. This blindness couldn't be counteracted because it is not itself magical (though it might be cured by other magic, such as sound body).
If a spell's caster dies or is incapacitated during the spell's duration, the spell remains in effect until its duration ends, using the caster's initiative order.
Some spells have effects that remain even after the spell's magic is gone. Any ongoing effect that isn't part of the spell's duration entry isn't magical. For instance, a spell such as sunburst that creates a brief, intensely bright flash of light might blind someone for a time, even permanently. This blindness couldn't be counteracted because it is not itself magical (though it might be cured by other magic, such as sound body).
If a spell's caster dies or is incapacitated during the spell's duration, the spell remains in effect until its duration ends, using the caster's initiative order.
Sustaining Spells
Source Player Core pg. 300
If the spell's duration is “sustained,” it lasts until the end of your next turn unless you use the Sustain action on that turn to extend the duration of that spell.
Long Durations
Source Player Core pg. 300
If a spell's duration says it lasts until your next daily preparations, on the next day you can refrain from preparing a new spell in that spell's slot. (If you are a spontaneous caster, you can instead expend a spell slot during your preparations.) Doing so extends the spell's duration until your next daily preparations. This effectively Sustains the spell over a long period of time. If you prepare a new spell in the slot (or don't expend a spell slot), the spell ends. You can't do this if the spell didn't come from one of your spell slots. If you are dead or otherwise incapacitated at the 24-hour mark after the time you Cast the Spell or the last time you extended its duration, the spell ends. Spells with an unlimited duration last until counteracted or Dismissed. You don't need to keep a spell slot open for these spells.
Dismissing
Source Player Core pg. 300
Some spells can be dismissed, ending the duration early. This requires the caster or target to use the Dismiss action.