Its very fast with an SSD drive. The more noticeable improvement is boot time - with SSD you can be booted up to the desktop and ready to use in 10-20 seconds from cold boot, compared to maybe 50-60 seconds for a new laptop. Of course that alone is vanity more than anything else.
However, a lot of people don't realise that normally the bottleneck in any computer is almost always the hard drive - if your computer is ever slow and you look in task manager > performance monitor > disk you will more often than not find that disk queue is very high (10+) and that the computer is actually waiting for data to be written from and too the disk.
Even sometimes when you look in task manager and your CPU is maxing out, this is often a knock on effect from disk not being able to cope and upgrading to SSD can also solve this.
So bottom line is that with SSD drive computer will perform much better.
Also, quite often I buy lower spec machines for customers (lower end i5s or i3s for example) and then put an SSD drive in, and they will out-perform higher spec laptops with spinning disk drives (Especially as some computers also still come with 5400rpm spinning disk drives).
Edit: Also, not as important, but with an SSD drive the laptop will run at a lower temperature as well, less heat generated from an SSD drive than from a spinning disk drive.
