HDD (Hard Disk Drive) - The amount of space you have for your website. If your hosting plan or VPS does not include the amount of space you need, you will not have enough room for all of your website files. Some hosts offer "Unlimited" space, but remember, there is no such thing as a hard drive with unlimited space. There is always a catch somewhere in the fine print.
SSD (Solid State Drive) - Hard drives with no moving parts. These drives are more efficient, use less power, and run cooler. They also have a much faster Read/Write time. If your website is mainly static file, there is not much benefit to using SSD. However if your website uses a lot of database queries, then switching to SSD's can improve page speed.
CPU (Central Processing Unit) - This is the power of the server. If the processor is not powerful enough, it will not be able to process information fast enough to keep up with the load. This is not something you will have to worry about with shared hosting. VPS's typically give you a certain number of CPU Cores. If you are looking for a dedicated server, this is where you will need to compare processor chips. i class chips (i5, i7) are made for desktop computers, Xeon processors are better for web hosting.
RAM (Random Access Memory) - This is the memory the server uses to hold information that it may need later. A computer can Read/Write info to/from memory hundreds of times faster then it can to a disk (Even a SSD). You always want to make sure you have plenty of available RAM to handle tasks. As you get upwards of 70% RAM utilization, you can have problems with services shutting down, freezing up, or lagging.