Potatoes, like most root vegetables, are hard and starchy, which means they store well in a cool, dark location. The downside to the potato's hard texture is that potatoes need at least 30 to 60 minutes to cook, depending on the cooking method. You'll definitely want to pierce them with a fork to determine if they're tender, but poking them with a fork early won't drastically reduce the cooking time.
For baking, your mom probably taught you to prick potatoes before you put them in the oven or microwave. The main reason is that this allows steam to escape from the potato as it cooks. If steam builds up, potatoes may explode or collapse, which are two consequences you want to avoid. Pricking potatoes can help them cook a bit faster, because when you've pricked them, you have enabled heat to enter the potatoes more easily.
If you're boiling potatoes for a potato salad or mashed potatoes, the best way to accelerate cooking time is to cut the potatoes into 2-inch pieces. Larger pieces take longer to cook, while smaller pieces tend to absorb too much water and then break down in the water. Pricking them may cause them to cook faster, but don't overdo it, or the small pieces will break as they cook. If you have more time, try boiling potatoes uncut in their skins. They'll retain more flavor and nutrients, and they are a breeze to peel.
Piercing potatoes with a fork might speed up the cooking process, but other factors are at play here, as well. Certain types of potatoes are naturally harder than others are and take longer to cook. Russet potatoes, which are harvested in the fall, take longer to cook than new, red potatoes dug out of the garden in early summer. As potatoes age, they become softer, so they cook faster. Old potatoes aren't as tasty as fresh potatoes, though -- so, in this case -- fast cooking isn't a good thing. How you cook potatoes also influences their cooking time. Roasting cut-up potatoes at high heat takes less time than baking them at moderate heat. Convection cooking also speeds cooking time by about 25 percent.
Your mom probably wrapped potatoes in aluminum foil to bake them and maybe you follow that practice. The conventional wisdom behind this strategy is that baked potatoes cook faster when wrapped in foil, because foil transfers heat. Wrapping potatoes in foil before baking, doesn't make them cook faster, although it does keep them warm longer after baking. It also gives them a soft, tender skin, rather than a crisp, crackling skin.