Dark Souls is a fairly simple games composed of a few well integrated loops. I'm going to go over a few of them and explain how they flow together.

Combat Loop

The core loop of the game, attacking an enemy and dodging their attacks is the smallest loop in Dark Souls. The player's main options are multiple types of attacks (heavy, light, jumping, rolling, spells), rolling to dodge, and healing. Each action other than healing consumes stamina, which forces players to consider attack and roll conservatively. Attacks from enemies cause the player to stagger without sufficiently heavy armor, which can interrupt attacks.

Death Loop

Built into the game is the idea of learning the level's layout and enemy placements. This loop is very simple, the player dies, and tries again with their newfound knowledge. This knowledge may be trap placements or enemy attack patterns. This is the basis of how areas are explored and bosses are beaten.

Bonfire Loop

Bonfires function as checkpoints, resting at one resets almost all enemies and the players health potions, which are finite during combat. As the player progresses, they learn to play conservatively and not waste their resources until they find the next bonfire. 

Upgrade/Exploration Loop

Although many areas in the game are not hard-gated, as in, you do not need to beat the boss of another area before going to this area, the game discourages the player from going into these areas because the enemies have too many stats. There are also upgrade level limits that can only be passed with the correct ember (giving this ember to a blacksmith will allow them to level their weapon). The loop that results from this is as follows. 

Player discovers an area and figures out whether they can access it at all or combats enemies to find out the level of the area. If the enemies are too hard, the player goes to find other areas or explore current ones to level up themselves and their gear. Then, the player will try to explore the new area again and get more souls and oftentimes better spells, more souls, embers and/or upgrade materials. They can then use this newfound strength to discover new areas from that area or any other.

Credit to AdikDarkCero

Loop Flow

The central loop of Dark souls is the death loop. The knowledge gained through experience is fundamental to the game. Within the knowledge gaining section is the combat loop and the bonfire loop. Game progression stems from the bonfire loop and the upgrade/exploration loop.