There's different ranks of landed titles- Baron/Barony, Count/County, Duke/Duchy, King/Kingdom, and Emperor/Empire. Barons are not playable, so you are at least a Count.
At any rank, your demense (demense is based off of the word "domain" as in your personal domain) limit is limited and you can hold a few counties without penalty. If you have exceeded this limit, you need to create a vassal by granting one of your counties to another character (typically an unlanded courtier). This is done via the diplomacy menu, which you access by right clicking on a character's portrait (this also where other important interactions are). The problem however is that as a Count, you cannot have another Count under you so you need to create a Duchy title, which makes you a duke. If you look at the de jure map modes, you'll see all counties belong to a duchy, which in turn belongs to a kingdom, which in turn belongs to an empire. When you have 51% of a title de jure (de jure basically just means "legal"; if you're familiar with the other Paradox games this is the same idea as cores), you are allowed to create it. A notification will appear and then you will spend gold (and also piety if a kingdom/empire).
So yes, you do need to have vassals and you do need to create other titles. The game's goal is pretty much to accumulate wealth, titles, and prestige for your dynasty. Just remember though you can't hold it all for yourself, but you can you try and aim for characters with high stewardship or increase your centralization laws in order to hold more. Also, when you do have to give away titles be mindful of the de jure layout. Keep corresponding titles together if you can help it, since you'll end up angering your vassals since they'll desire those titles otherwise.
Finally, when you've grown larger to the rank of King, you'll want to give away duchy titles as well for the sake of organization. It also makes things easier to manage, since the vassals that are placed under another are no longer your problem. Therefore, the fewer vassals you have the easier time you'll have managing them. Of course, you have keep things balanced though. You do not want one or two powerful vassals that might later turn on you. Keep your vassals weak by only giving out one county per character and later a single duchy or kingdom.