Depending on who is writing the book...resurrection, its use, and commonality varies wildly. But, in general--resurrection is something that only applies to a very limited set of people. Adventurers and other sorts of Extremely Wealthy and/or Important individuals are the only people who the existence of this magic has any real impact on. But even then, not always
To understand the impact of resurrection magic in The Realms, you first have to understand this. Resurrection magic is expensive. And finding someone who can wield it may be quite difficult.
As adventurers, it's easy for players to lose track of the precise cost of things, because adventurers generally accrue money at an absurd rate.
The cheapest form of resurrection magic, Revivify, is basically useless to people who aren't adventurers. If a caster with access to the spell isn't right there when you die and has the 300gp in diamonds necessary, then this spell can't help you. So, for the larger population of The Realms, this spell is irrelevant.
Thus, the least expensive form of resurrection magic that really matters to the larger population is Raise Dead. Which requires a single diamond worth 500gp. Naturally, you must also locate and secure the services of a spellcaster able to use 5th-level spells. Probably a Cleric of 9th level or higher. Temples in a big city generally have a Cleric able to cast Raise Dead, so this isn't a huge problem...but understand that they will charge you for their services, on top of the material cost.
Using the derived equation for spellcasting services from the Adventurer's League, we can ballpark that hiring someone to cast Resurrection on you is going to put you out 250gp if you provide the diamond, or 1250gp if you do not.
So, assuming you get your own diamond...a skilled laborer pulls in about 2gp per day (PHB 159), if they live at a Modest Lifestyle and never spend money on anything else, they have to save money for 750 days to pull together enough funds to afford a Resurrection spell. And they have to have done this in advance, because Resurrection has a 10 day time limit on it. So, for a person to be Raised, they have to have a 500gp diamond and 250gp in liquid assets just lying around, untouched, in case they get killed and need to be raised. And hope really, really hard that nobody robs them.
Note: Page 159 of the PHB says that...
finding someone able and willing to cast a higher level spell might involve traveling to a large city, perhaps one with a university or prominent temple. Once find, the spellcaster might ask for a service instead of payment--the kind of service that only adventurers can provide.
In short: Normal people don't get raised from the dead. They can't afford it, and don't have the skillset to trade services for the spell. Only the wealthiest of the wealthy can afford it. And given that we're talking about a primarily feudal society...
You're talking high-end Nobility, highly successful Adventurers, people important to a church, and others supported by such people are the only sort who get resurrected.
Resurrection in The Realms
Surprisingly for the mechanics, but unsurprisingly for storytelling quality, resurrection magic hasn't seen a lot of use in the fiction surrounding The Realms. If you can raise your characters from the dead too easily, then death (and peril) loses its impact as a story mechanic. If you know going in that any character who dies can just be Raised...then the novel loses a lot of its drama.
There are a few instances of it cropping up, such as a short story called The Resurrection Agent about a sort of special agent whose whole job it is to spy, gather intel, gather evidence, then get themselves killed so that they can then testify against their killer after the organization that supports them recovers their bodies and raises them.
In other sets of fiction, Resurrection magic is hardly mentioned at all. There are numerous times is the Drizzt series where characters were believed to be dead...and everyone acted like this was permanent. In the Sellsword series, a much-beloved hero of the land died--and no one even talked about trying to resurrect him. In the Cormyr series, multiple rich people ended up dead and it was mentioned that 'the way they died' prohibited resurrection.
The latter is easy enough to understand. A murderer canny enough to know how resurrection works would know that if you take a critical part of your victim with you and destroy it (head, heart, etc), then the material cost to raise that individual just doubled, and now you're looking for someone who can cast 7th level magic. (Raise Dead doesn't regenerate body parts, Resurrection does). This is confirmed to be the case in Salvatore's Cleric Quintet series, where it clearly spells out that Assassins routinely steal body parts of their victims to inhibit resurrection.
A few instances where Resurrection Magic does seem to be more common have turned up. The Lady Penitent series shows worshipers of Eilistraee being raised left and right. And the Mulhorandi goddess Osiris has an entire order dedicated to her composed exclusively of those who have been Raised after being killed by a worshipper of Set. Additionally, on Page 35 of the sourcebook Waterdeep: City of Splendor, it specifies that the City Watch will pay for your Resurrection if they kill you while trying to arrest you, then later determine you were innocent of any crimes. (Admittedly, doing something that forces the City Watch to kill you is probably a crime in and of itself...so this probably doesn't come up much).
One notable example that is a bit...odd...is Elminster. He's been 'killed' and 'mostly killed' and had all manner of other horrible things happen to him. But Mystra keeps putting him back together. (see Elminster in Myth Drannor) It's not quite use of Resurrection Magic. More like divine intervention.
In the fiction around The Realms it seems like the use of Resurrection Magic varies wildly depending on who is writing the story. Oftentimes there are points where important people end up dead, and no one even thinks about looking for a Cleric to pop them back to life (even if they were rich enough to afford it). In others, resurrection spells get tossed around pretty commonly. And in yet others, resurrection spells are attempted, but fail due to 'side effects' or 'other reasons' that are not actually supported by the D&D game mechanics.
As far as we can tell, the overall impact of Resurrection Magic is fairly minimal in The Realms. Heroes, Nobles, and Kings die and stay dead. Whether this is because they can't afford the resurrection spell, or can't find a Cleric able to cast it varies.
The magic to raise the dead exists, but doesn't apply to the vast bulk of the population on account of price and the rarity of Clerics powerful enough to wield that magic. So, yes...there are examples of heroes being raised from the dead--and there have been instances of Nobility being raised as well. But, it is still uncommon enough that it isn't world-shaking in nature.