There's probably a lot of parts that contribute, but I'll give you a few that I've noticed help a lot:
Fewer circumstancial bonuses
You don't need to remember a ton of minor bonuses, like getting +2 for flanking and +1 against Goblinoids and +1 from your Feat and -2 from being shaken. Every roll is a basic, set amount and you either roll with Advantage, Disadvantage, or neither. And both Advantage and Disadvantage just means rolling twice and picking the higher/lower roll respectively.
This massively cuts down not only the amount of bookkeeping and remembering you need to do, but also decision making. You won't have to try and squeeze out every last stacking +1, you can just look for a single way to have Advantage, grab it, and swing away.
Less stacking of spells
With each caster being limited to a single instance of Concentration, and most longer duration buffs requiring it, the number of spells active at the same time is a lot lower. This means less things you need to keep in your mind, and again less decision making and pre-battle buffing. You can focus on maintaining the one spell that really matters.
Tied into this is the new spell preparation system, where you separate which spells you could cast from which ones you do cast. This means that if you decide to prepare Magic Missile, you can during the day use anywhere between 0 and all your spell slots to cast Magic Missile. That means combat decisions get cut from "Do I spend my only Magic Missile for today on this?" to just "Do I spend a level 1 Spell Slot right now?" which is an easier decision. It also means you can more easily decide a useful buff right now instead of waiting for the perfect opportunity because you only have one. That makes it much quicker to see what the best move is at a given time.
You tend to do a few things really well
Most characters have a few options that they are really good at, with no mechanically complex but ultimately minor bonusses. A great comparison for example is the new Rage mechanic for Barbarians.
You no longer need to recalculate your Strength, Constitution, AC, (circumstancial) saves, abilities, attack rolls, damage rolls, and hit points in order to decide what going into a Rage does.
You just add +2 to damage, get advantage on all your Strength and Constitution saving throws and you take half damage from weapon attacks. Easy to apply, thematically perfect, mechanically powerful.