One of the challenges in Dungeons & Dragons when playing an arcane character class is the limit of spells that can be cast per adventure day.
Usually this divide breaks down between wizards and sorcerers- wizards having more spell selection but less casts per day, while sorcerers have more casts but less selection.
Regardless there is a finite pool of spells, even when taking in account feats, power boosts, and other ways to get more spells per day.
Regardless of the base, the only way to recover spells is to *rest*, which is really dependent not only on the Dungeon Master, but also on the adventure.
Some DMs will let you rest and time and place to get spells back, a few will be very specific, and many take the middle road with being reasonable plus random encounters.
In terms of encounters, unlike fighter and warrior classes who can swing away every turn, mages need to get the most out of each spells.
Which leads to area-effect spells and radius spells- the chance to catch multiple targets at the same time- sleep, color spray, fireball, etc.
Being able to engage and take out multiple monsters, equals that many swings from a warrior class.
As a arcane caster, keeping a mix of direct attack and radius spells to get the most possible cast effects per day.