Reading and writing database information can be slow, especially if you have a large database and/or multiple users hitting the data at the same time. It's rare that the information that you want to retrieve from a database is stored sequentially. As a result, the hard drive has to go find the information that you requested.
Rotational drives (HDD) have to physically move the heads to different positions over the drive surface in order to access the data, and they also have to wait for the desired information to rotate around underneath the heads. The time required to retrieve any specific piece of information from a modern rotational drive is about 10ms. While a hundredth of a second doesn't sound like much, it adds up very quickly when you have to do thousands of reads and writes from different places on the drive.
SSDs don't have any physically moving parts, so it doesn't have to wait for the heads to move or the data to rotate under the heads. While the access time varies between SSD manufacturers, a 0.1ms average access time or better is quite common with newer SSD drives.
Now for a little math. If your operation requires 100,000 read/write operations throughout the average day, that comes out to about 16 minutes of time waiting for the data to be accessed on a HDD with a 10ms average access time. Those same operations on a SSD with a 0.1ms average access time is less than a minute. 15 minutes of wasted time is not insignificant.
Is it time for a SSD? The answer to this is a bit subjective, but it's not a difficult question to answer. If you have a rotational HDD and the data access is sluggish enough that it is affecting the efficiency of your operation, then moving to a SSD can save you significant time and money. Back to the math. If you lose 15 minutes of productivity a day from the wait time of your HDD and your average hourly wage for your employees is $15, your HDD is costing you $3.75 a day in employee time. With the cost of 500GB SSD drives being under $200, it doesn't take much in time savings to more than pay for the upgrade.
Keep in mind that access time is only one portion of the time it takes to read and write data from the database, so your mileage may vary depending on your environment. But it's pretty clear that a SSD drive can make a significant difference in performance with a minimal investment in some new hardware.