You may mistake challenging and difficult as being synonymous, but acknowledging the difference is key in the enjoyment and appeal of a game. A challenge is the test of your ability, whereas difficulty requires great effort or skill in order to accomplish a task, often requiring a lot of time. Think of it like this: challenge is the steep slope, whereas difficulty is the brick wall.
When the subject of difficulty in games comes up, Dark Souls is often the first game to be mentioned, so let me do the same. Dark Souls and its awkwardly-named predecessor Demon's Souls are not challenging games, they're plain old difficult. I'll explain why after I do a side-by-side comparison with Super Meat Boy in terms of difficulty vs. challenge.
Super Meat Boy is a game that will send many into a rage, but if you do get eviscerated by a flying saw or swallowed by a salt pit, it's not the games fault, it's yours. The controls are taut and the presentation is clear enough for you to distinguish a hazard from a platform. The designers know that you will die a lot in the levels of Super Meat Boy, so the levels are short and plenty and the respawn time is almost non-existent. It's trial and error, but the error isn't heavily punished since the game knows that three out of four walls are deadly. The punishments for your error are a) losing your progress and being sent back to start and b) being frustrated with yourself for not being able to surmount a simple obstacle. You know where the hazards are and where not to fall, and there are no cheap, unexpected, one-shot insta-deaths, so when you die and have to restart, it's never the games fault. Super Meat Boy blissfully manages to be challenging without being frustrating.
Dark Souls is full of stupid, cheap and unexpected deaths, with insta-killing barrels rolling down staircases with little to no warning. It's organic, sure, but in a way that you can't distinguish a hazard from an objective. When the bosses do come (namely the second one) with no time or warning for you to prepare, they surround themselves with archers and always always one-hit-kill you. And when you do die from unexpected, unfair deaths, you're set back right to the start. That wouldn't be a problem in Super Meat Boy where the levels are short enough for you to recover and learn from, but in Dark Souls, levels are extremely lengthy and arduous, so being set back right to the start with all enemies reset and all progress lost could not be more frustrating. It's not intended for you to overcome a challenge, it's just being plain old mean. A lot of people will disagree with me on this, but Dark Souls is not a challenge, nor is it testing your skill, it's testing your ability to put up with being bullied. To quote Yahtzee Croshaw, "A challenge is one thing, but trying to break down a cement wall with your forehead isn't a challenge, it's grounds for getting sectioned."
Other games can pull of being challenging without being frustrating, like many levels in the most recent Rayman games. The auto-saving is just the right amount of frequent and the controls are taut and a pleasure to behold, allowing you to recover and learn from previous errors. You might say that that's what Dark Souls does; you have to play the level multiple times in order to become familiar with it and learn all its tricks, to which I say, and for what? The skills you learn in previous levels will not help you in later levels because the levels drastically change and the tricks become more varied, more common and even trickier. Learning your way around a hazard or an enemy in Super Meat Boy will help you later on because perhaps that same hazard or enemy may appear in a later stage, like a boss fight. The boss fights in Super Meat Boy are the best kind of boss fights. They're the kind that test your ability and knowledge up to that point, and leave you with a sense of accomplishment. You could say that that's what Dark Souls also does, and I reckon it does, but the only meaningful progress you would make in a level of Dark Souls is a higher tolerance for nastiness, and the boss fights test your tolerance, and surmounting a boss will give you a greater sense of accomplishment. But that's not all there is to a boss fight, or a game as a whole for that matter.
The point of Super Meat Boy is to have fun in facing a challenge, and it pulls it off with flying colours. I'm sure Dark Souls is engaging to the masochistic audience of gamers, but that's not me. I'm glad that games like Dark Souls exist for those that want a high barrier to entry, but that's not fun or engaging, it's just to show off to the internet that you can. If you like being punished by games with a high barrier to entry, that's fine, but understanding the difference between challenging and difficult is important to understanding what games you prefer to play as a consumer and what audience of gamer you're making your game for as a designer.