I know the thrust of the topic is for Super Mario Bros., but it's important to note that Mario's earlier adventures are also solid.
I think it's due to how deep the gameplay is, even when there are not many outputs. The original Donkey Kong has just a control stick and a jump, but the stage layout presents a unique obstacle course that makes use of the controls. Mario can use his jump to go over obstacles like barrels and gaps, and he can also climb ladders and navigate elevators. And then Mario Bros. made Mario jump higher, and provided him with another layer of offense by bumping foes from the bottom. Even the position that you bump the enemy affects their trajectory! Not to mention: the different types of enemies and hazards, and they need to be tackled differently, which creates a game where many can happen at once, but still being approachable. I don't think Super Mario Bros. could've been the way it is if it weren't for the foundation set by the predecessors. The gameplay foundations is one thing, but if it weren't for Mario games being fun and selling well, there would never have been a Super Mario Bros., because the reason it's a Mario game to begin with is that Mario Bros. for the NES sold well, prompting Tezuka to make the next game about Mario. Imagine if it were Super Ice Climbers instead... it would probably not be as great as Mario is now.
Another aspect that Mario does well is how character-oriented the games are. Of course, Mario is designed to be recognisable on the screen, but you also have the various objects that have their own unique designs and cues. For example, the angry disposition of Donkey Kong, the fireballs with eyes in Donkey Kong, the angry crabs when they're hit in Mario Bros., and so on. Even Super Mario Bros. injects personality into its enemies, like how the Red Koopa Troopa's won't walk past a ledge, Bloopers gradually float towards the player, and Piranha Plants that emerge from the pipe but won't if the player is too near. It certainly add to the games compared to if some generic obstacle were used. The character, combined with unique behaviour of the enemies, gives the game some life in the variety it provides.
For Super Mario Bros. in particular, I think it just have a lot to it that makes it feel like something is hidden in the corner waiting to be discovered. Like for example, if you chain enemies with a jump or a shell, you can rack up points and even get 1-Ups from them. Another thing is hidden blocks, especially if there are 1-Up mushrooms in them. Special mention goes to the coins. Coins are a recognisable thing to collect because we know that money is good to have, and they facilitate the exploration by rewarding them. Those blocks with multiple coins is one thing, but secret rooms tend to have many coins as a reward for finding them. Heck, hidden stalks tend to lead to the skies with many coins!
I guess the old Mario games are taken for granted these days, but it's important to know that if it weren't for the old games holding up, Mario might not be where he is today: a 41+ year old video gaming icon that is active throughout the years.
Thank you for reading.