On Facebook, it is possible to unblock a person that you had placed on your blocked list.
Steps
Method 1 of 2: Unblock people on iPhone or Android

Step 1. Open Facebook
This is a dark blue app with a white "f". If you're signed in to Facebook, your news feed will open.
If you are not logged in, enter your email address (or phone number) and password first to continue

Step 2. Press ☰
This button can be found in either the lower right corner (iPhone) or the upper right corner (Android) of the screen.

Step 3. Scroll down and select Settings
You will find this option towards the bottom of the menu.
Skip this step on Android

Step 4. Choose Account Settings
This option is located either at the top of the popup menu (iPhone) or at the bottom of the menu ☰ (Android).

Step 5. Select Blocking
This option is near the bottom of the screen, next to a "no entry" sign.

Step 6. Tap Unblock to the right of someone's name
On this page, you'll see the list of people you've blocked. You can choose to unblock people.

Step 7. Choose Unblock when prompted
It's a blue button located on the left side of the page. This will unblock the person you selected.
If you want to block that person again, you will have to wait 48 hours for this to be possible
Method 2 of 2: Unblock people on Windows or Mac

Step 1. Go to the Facebook website
Go to If you're signed in to Facebook, your news feed will open.
If you are not logged in, first enter your email address (or phone number) and password at the top right of the page

Step 2. Click ▼
This button is located in the upper right corner of the Facebook window.

Step 3. Choose Settings
This option is near the bottom of the drop-down menu.

Step 4. Select Blocking
This is a tab located on the left side of the page.

Step 5. Click Unblock to the right of someone's name
You will see the list of people you have blocked in the section Blocked users.

Step 6. Choose Confirm when prompted
This will unblock the person you selected.