The particular generation algorithm that you see is called "Randomized Prim's algorithm" on Wikipedia. It starts at a random cell in a grid, marks it as discovered, and adds all of that cell's adjacent walls to a queue. It then selects a random wall from the queue and, if the cell on the other side of the wall has not yet been discovered, opens up that wall. It adds all of the adjacent cell's walls to the queue, marks the adjacent cell as discovered, and selects the next random wall in the queue until all the cells have been discovered. It's kind of a modified BFS. This algorithm guarantees that all cells are connected.
Most maze generators build a giant tree, starting from an arbitrary point and sending out branching corridors until the area is full. By its nature everything's connected.