It is a storage device, with the same purpose as HDD (hard disk drive). However, unlike HDD, it has no moving parts and consists of purely electronic components. When you install Windows to an SSD, you get much faster operation in general, since storage performance is usually the biggest bottleneck in any system. This is especially true for laptops, where HDDs are even slower than on desktops, so using an SSD instead of HDD is a huge improvement in overall performance (system loading, app and game loading, general tasks).
The only "problem", so to speak, is that SSDs are more expensive per gigabyte of capacity, but this improves every day and the gap is slowly closing.