Unless a super small mini or micro PC, the vast majority of desktops computers have more than one video output connections on the back. They may be two different types, HDMI and DisplayPort, for example but typically you can connect a monitor to each and use them as one big "extended" desktop. Then you can have an open Word document on one monitor and your email program running on the other. You can move windows from monitor to monitor, even copy a file on one monitor and paste it in a folder on the other monitor.
I've been running a dual monitor setup for over 25 years and frankly, I don't understand how anyone can live with just on monitor.
If your computer does not have two video outputs, you will need to add another adapter. A card would be best, IMO, but there are USB types too. The problem with a card is it may require upgrading the power supply too.
As noted, a splitter takes one signal and sends the same image to both monitors. Anything you do on one monitor is replicated on the other.