Read this article to learn how to change a Facebook group's description via a web browser.
Steps
Method 1 of 2: Editing on the Group Page

Step 1. Access Facebook in a web browser
You can also type “http://www.facebook.com”, without quotes, into the address bar and press the ↵ Enter key. The social network will open and you will see your News Feed.
If you are not logged in to Facebook, you will need to provide your email or phone number, as well as your password, to login

Step 2. Click on the search field
It will be at the top of the screen in the menu bar.

Step 3. Search for the group you want to edit
Matching results will be displayed in a drop-down list as you type.

Step 4. Click on the group name in the list and you will be taken to their home screen
When the group you are looking for does not appear in the drop-down list, click the magnifying glass icon. All matching results will be displayed

Step 5. Scroll down the screen and click Edit next to “Description”
The description for that group will be displayed further to the right of the screen, under “Members” and “Suggested Members”. After clicking on “Edit”, it will be possible to change the description on the group's home screen without changing other information.
- If there is no description, the button will be “Add a Description”, not “Edit”.
- Only admin users can change the group description. The “Edit” button does not appear for those who do not have administrative privileges.

Step 6. Click and edit the text field
It is possible to modify or delete the current description, allowing you to compose another one.

Step 7. Click Save
Changes will be saved in the group description.
Method 2 of 2: Editing from the “Groups” Menu

Step 1. Open Facebook in a web browser
You can also type “http://www.facebook.com” without quotes into the address bar and press the ↵ Enter key, and you will automatically be taken to your profile's News Feed.
You will need to provide your email or telephone number, as well as your password, to login if you have not yet logged into your account through this browser

Step 2. From the left navigation menu, click on Groups
The button will be in the “Explore” section of this panel to the far left of the News Feed.
If “Groups” does not appear in the menu, click on “View All…” at the end of the “Explore” section

Step 3. Enter the Groups tab, which will open, in turn, to the “Discover” tab
Click on the “Groups” tab, just below the Facebook logo in the upper left corner of the browser, and a list with all the groups you are a part of, including administrative privileges, will be shown.

Step 4. Find a gear icon next to the group you want to edit
In the “Groups you manage” section, look for the one that should have the description edited and click on the gear. Administrator options will be displayed.
You can only change the description of groups you manage; normal members cannot edit their data

Step 5. Click Edit Group Preferences
The “Group Information” page will be displayed, allowing you to change the following data: “Group Name”, “Icon”, “Type”, “Description”, tags and geolocation, among others.

Step 6. Click and edit the text field next to “Description”
Here, you can modify the group's current description, or even delete it and write a new one.
Step 7. Scroll down the screen and click Save at the bottom of the group information page
A notification will appear saying “Changes have been saved” at the top of the browser window.