Please check the following for the difference between Profile and Permission Set in Salesforce.

Profile:

A profile contains user permissions and access settings that control what users can do within their organisation.

Permission set: 

A permission set is a collection of settings and permissions that give users access to various tools and functions.
Permission set enhances functionality of profiles,
Consider a scenario where only one user need access to “Case” object and he belongs to some ‘Sales’ profile, then we need to modify that profile which will affect other users with the same profile.

So, alternatively we can create a permission set with access to case object and assign that to that particular user.