In your Personal Setup (Classic: Your Name > My Settings, or Your Name > Setup > My Personal Information, Lightning: Your Icon > Settings), you'll see an option for Advanced User Details, on the left under My Settings > Personal. Alternatively, use the Global Search box to type in your name, then click to bring up your Person profile, then click on User Details.
On this page, the right-hand column should have a field called Profile. This tells you what your current user profile is. Clicking on it will take you to a page that shows you all of your permissions under this profile.
Scrolling down will take you to a section for your Permission Sets, which are additional permissions assigned to your user atop your Profile settings. You can only have one Profile, but you can also have many Permission Sets assigned to you.
Some or all of this information may be hidden if you don't have certain permissions enabled (such as View Setup & Configuration). In that case, you'd need to contact a System Administrator.