A Permission Set is a bundle of permissions you assign to users. A Permission Set License (PSL) is a prerequisite licence that some advanced features require before a permission set can grant them.
Concrete example: to give a user the "Sales Console" feature you need both (a) a Sales Console permission included in a permission set, and (b) the Sales Console PSL assigned to the user. Without the PSL, even if the permission set is assigned, the feature stays dark.
You see PSLs in the Setup -> Company Information -> Permission Set Licenses table — Salesforce lists how many of each you've purchased and how many are assigned. Examples: CRM Analytics Plus PSL, Identity Connect PSL, Sales Engagement PSL, Field Service Mobile PSL.
A common admin headache: someone gets a permission set, but the feature still doesn't work. Check whether the permission set requires a PSL the user doesn't have. Salesforce shows a warning in the permission set UI when a permission requires a PSL the org hasn't purchased, but for assigned PSLs the issue silently surfaces as "feature missing for some users".