Flowers are a plant's way of producing new seeds. Blooming is a normal, healthy process that can happen year after year for most succulent varieties and attract pollinators to your garden.
The exceptions are Sempervivum, Tillandsia (Air Plants), and some Agave. These types of succulents are monocarpic, meaning that each plant can only bloom once in its lifetime. Fortunately, they will grow for many years and produce offsets before blooming out.
For Sempervivum, you can temporarily halt the blooming process by scooping out the bloom stalk with a sharp, clean knife. This only works if you catch the bloom stalk as soon as it starts to stretch and it will not prevent flowering indefinitely. Cutting out blooms will not return you to the single, perfectly symmetrical mother hen you started with, but it can give you more offsets to transplant before the original rosette eventually dies.
For more information on Sempervivum flowers, what triggers blooms, and how to temporarily prevent them, check out the full Visual Guide to Sempervivum Blooms.