The arrow icons under each post and comment are voting buttons. The number in the gray circle to the left is the total number of votes a comment has earned. Voting is your way of anonymously voicing your opinion and impacting the content posted by the community. By voting, you help the Duolingo community remain a clean, safe, and interesting space.
The upvote button
When you like or agree with a comment, or if you think it was helpful to you, click on the up arrow to the left. The icon will turn green and the commenter will know your appreciation. The most voted comments are the most popular, and will float up to the top of the comment thread. You can undo this action if you selected it accidentally—all you have to do is click on it again. This is useful in order to show your praise and appreciation in a considerate way by avoiding too many follow-up comments that do not add to the conversation (such as "haha"/ "lol"/ "I agree!"/ "Thanks!"/ "You're right"/ etc.). This feature is especially useful under Sentence Discussions, where you can upvote comments containing the same question you had (not just the answer), so that the most common questions are easier for people to find when accessing the discussion.
The downvote button
When you don't think a comment adds to the conversation and think it should move further down in the thread, click on the arrow that points down. You will remove a vote from the count and the comment will become less popular. If a comment receives too many negative votes, the system will move it to the bottom of the thread and eventually hide it from immediate view. Use this for offensive posts, personal attacks, harmful content, and spam. Depending on the content, the comment may be deleted by moderators.