By way of an overview in case you're not too computer-savvy:
Normal hard drives like the one most likely fitted to your laptop contain spinning platters that contain the data you store. By virtue of their need to spin they include a motor that makes noise, usually fairly high-pitched because the drive spins very quickly, usually at either 5400, 7200 or in some cases 10000rpm.
Solid State Drives (SSDs) by comparison have no moving parts at all, consequently they're entirely silent. That's a great benefit to them but their primary benefit is performance. While a normal drive relies on a mechanical seeker head moving to the correct location on the disc and reading the data from it, which takes time (and causes noise), an SSD works similarly to your computer's memory, working silently and extremely quickly. It doesn't work quite as quickly as your computer's memory but nearly, and certainly much quicker than a conventional drive would.
As the others have already said, the 'problem' is most likely to be the fan. Laptop cooling systems use heat pipes to transfer heat from the components in your system that need cooling to a heat sink. The fan then draws cool air from outside the laptop in, blows it over the heat sink and then exhausts it out the side or back, but, there's a catch-22 situation going on. To make a laptop compact the heat pipes and heat sinks need to be small, but to make them cool efficiently that relies on a fan that can shift a lot of air. To make a small fan shift a lot of air it needs to spin quickly, hence the noise. So, you either have a laptop that's thicker, but runs more quietly, or a thinner one that runs noisier. Obviously that's a very general statement; components, performance, quality, workload, all these and more affect the size and noise of your laptop, but as a general guide it's close enough to give you an idea of what's going on.
You could, as a test, install a program called SpeedFan. That will give you control over your laptop's fan speed and will show you what rpm it's spinning at. You could, temporarily, and while keeping an eye on temperatures (which SpeedFan will also tell you), lower the fan speed and ascertain once and for all if it's the fan that's causing your noise problem.