Since version 13.2.49.79 no plan waits for an approval and nothing stops because a plan has not been approved: a plan says where the project is going, and the agents keep their work in line with it. What still binds every agent is the Rules, see What is the Rules tab, and why should I write rules?.
The thumbs-up is a vote that tells the team and the agents which plans you prefer. On each plan not yet completed, in its row and in its side panel, the thumbs-up shows how many votes the plan has, for example 3: an outline when you have not voted for it, filled when you have. Click it, or reach it with Tab and press Enter or Space, to vote or to take your vote back; each person has one vote per plan. Everyone who can see the project's Planning can vote, the owner and the managers alike, while agents never vote. The side panel says who voted, for example 3 votes · Andrea, Salvatore, or No votes yet.
The most voted plans come first, in Planning and in what the agents read, and among plans with the same votes the most recently changed comes first. A vote is not an Activity entry, makes nothing unread and sends no notification; it stays when the plan is changed. Only the votes of the people who are in the project now count: the vote of someone who leaves stops counting, and counts again if they come back. The approvals given before version 13.2.49.79 became votes, one for each person who had approved a plan. See What is Planning in SyncNow?.