In my campaign (me being DM) one of my players entered an adventuring gear supplier, and they wanted to buy something. They asked “What does a tent do?” And the only thing I could think of was that it protects you from monsters in the night.
So what does a tent actually do? What benefits does it give a character?
It does what a tent does: provides temporary shelter from rain, snow, wind, cold, sunlight, and so on. Depending on the severity of these conditions, the lack of such shelter could create a situation where restful sleep is impossible. In the absence of restful sleep, most humanoids accumulate levels of exhaustion, which is debilitating and eventually lethal. The conditions themselves, if severe enough, could even be life-threatening (leading to hypothermia, sunstroke, etc.).
Privacy.
It is possible, during your nights in the wilderness, that there might be some things you wish to do that you would rather not be observed doing. This might be plotting to cheat your fellow adventurers, discussing who might be the enemy infiltrator, preparing spells without being disturbed, or.....other things.
Status
Nobody else has a tent? You must be the big shot. If you can persuade someone else to set it up for you, then even more so.
In addition to the answer by @sptrashcan referring to sleep and exhaustion levels (refer to XGtE pgs 77-78), there may be a benefit to having a tent when faced with Eldritch Storms.
The description of a tent is as follows, emphasis mine (PHB pg 153):
A simple and portable canvas shelter, a tent sleeps two.
The descriptions of Eldritch Storms indicate that they cause damage to exposed creatures, however most of the storms do not deal damage to objects. For example, the description of a Flaywind indicates the following (TCoE pg's 163-164) :
a creature exposed to the storm takes 1d4 slashing damage at the start of each of its turns. Only substantial cover or shelter offers protection against the flensing grit.
Given that a Flaywind lasts for 1d4X10 hours, the damage could become quite severe.
DM Discretion
Accordingly, depending on how the bolded quote is interpreted by the DM, the tent may provide a benefit with respect to a flaywind. It would be up to the DM to decide 1) whether "substantial" refers to the shelter, and if so, then 2) whether a canvas tent is "substantial". Had the bolded been written "Only shelter or substantial cover offers protection against the flensing grit" (or if the description of a tent indicated it provided "substantial shelter") then there would be no doubt. see note below
Other Eldritch Storms
Finally, it is possible a tent would also aid with other Eldritch Storms including a Necrotic Tempest and a Thrym's Howl. The descriptions of those storms do not refer to shelter, however they do refer to "any creature exposed to the storm" taking damage. Again a DM could rule that the the shelter of the tent means that the characters are not exposed to the storm and are protected from taking that damage. On the other hand, the tent would likely be destroyed by a Flame Storm, which description indicates objects (that are not worn or carried) are ignited.
note: one reason to lean towards "substantial" only referring to "cover" would be that the shelter provided by a tent is never described in any kind of varying degrees. In other words, as long as the tent itself has not taken damage, then it functions as shelter. Whereas (assuming the designers are using the word "cover" as it is defined in the rules of Combat per PHB pg 196) cover has varying degrees including 1/2 cover, 3/4 cover, and total cover, in which case the descriptor of "substantial" would make more sense.
