Since Metal Gear Solid Delta takes its cues quite literally from the original Metal Gear Solid 3, it only makes sense that its difficulty modes would be similarly varied and flexible. This is no straight shooter, after all, but a highly complex and intricately built stealth game. Challenge comes part-and-parcel with this approach, but the good news is that you can scale it up and down however you see fit.
Delta: Snake Eater has 6 unique difficulty settings to choose from, ranging from Very Easy to... uh, European Extreme. Some are self-explanatory, while others take a fair bit of context to make heads and tails of. We'll explain all of them below, but there are a few important tidbits to keep in mind in a broader sense:
The second statement's going to make more sense as we approach difficulties higher than Normal. So, let's get to it.

Very Easy mode is perfect for those who just want to experience the gameplay loop and the story without any blockers or challenges. With a massive health pool, frankly slow enemies, and the EZ Gun in tow, Naked Snake is going to easily complete the Snake Eater mission.
Easy is a more sensible choice for those who want some friction, albeit not too much of it. The lack of the EZ Gun is the biggest detraction here compared to Very Easy, but you're still getting a very straightforward and delightful experience overall.
The default difficulty level for MGS Delta, Normal is an excellent baseline for the vast majority of players. This is the game at its arguable best, with a reasonably challenging experience that shouldn't, for the most part, ever get offputtingly difficult. Crucially, playing the game at Normal difficulty unlocks the DOBERMAN player title if you complete the game at under 5.5 hours without using any Special Items or LIFE medicine. That's not for the faint of heart, though, so we recommend going for the achievement during a New Game+ playthrough or some such.
We're still in the 'reasonably challenging' territory with the Hard difficulty mode, although this is absolutely where the going starts getting tough for Naked Snake. Enemies get a reasonable buff in basically all respects, Snake gets way fewer gadgets to fiddle about with, and trying to get the FOX title is no mean feat! To unlock it, you need to beat the game in 5 hours or less, without losing more than 5 LIFE bars, without using any Special Items, and without resorting to using LIFE medicine. Tricky, but doable for sure.
Extremely difficulty is not for those who want a reasonable challenge if you ask us. This is for truly skillful and experienced Snakes who know what they're up against. We also recommend completing the game at least a couple of times before even attempting to get the Extreme playthrough going, as the accrued New Game+ gadgets and game knowledge are going to be crucial for any amount of success. Further, the FOXHOUND title sounds sweet, but good grief is it a challenge to unlock. To get it, you'll need to complete an Extreme playthrough in 5 hours or less, you can't lose more than 5 LIFE bars, can't use any LIFE medicine or Special Items, must not alert any enemies, use any Continues, or kill anyone. Neat!
For those who think 'Extreme' is fiddlesticks, European Extreme is here to spice things up. All of the modifiers from the former difficulty setting apply here, but you must never be detected by anyone, ever. Simple as. Have fun giving it a shot, if you are so inclined. We'll stick to Hard, thankyouverymuch.
Wait, European Extreme? What?