This article has an interesting breakdown of level design and how to teach your audience about how to play a game without the use of lengthy dialog or heavily guided tutorial.
The author brings up how the entirety of the Super Mario Bros. series is centered around the verb “Jump.” By boiling the game down to its main action, a game designer can design levels to reinforce that while teaching the core concepts for the game. The beginning levels for Mario teach all of the most important points of the game, and they are all derived from his basic jump. Mario’s jump can kill enemies, break bricks, activate “?” blocks, etc. and the audience does not question it because it feels natural to the core of the game.
By introducing all the core concepts to the game early (avoid/jump on enemies, break bricks, get mushrooms, etc.) the game is able to introduce more difficult trials like jumping over pits and sequences with falling obstacles.
You can see this kind of introductory guidance in a lot of games of that era especially including Mega Man, Metroid, etc. The levels are designed around guiding you towards certain areas visually and teaching you about the core mechanics of the games. In Mega Man this is shown by for example, having certain enemies that spawn slightly above you, but who cannot hit you at first, allowing the player to get used to jumping and shooting. They also have levels designed around directing Mega Man to fall into certain corners of the stage to avoid enemies, which in turn teaches the player how to maneuver in mid-air. This combined with the jumping and shooting inherently builds a skill set for the player to allow them to maneuver around difficult bosses and complex levels just from combining the three main actions: Jumping, Shooting, and Moving in-air.
By teaching the audience to play your game without hand-holding them through a tutorial, the player often feels more comfortable in their own ability to play the game because they have better internalized the controls. In addition the players feel like they have really earned their place in later levels because they feel that they learned and developed their skills without being explicitly told what to do.