Daily Objectives were introduced in the Heists Update. They unlock at Rank 15 and players receive GTA$ and RP for their completing.
To complete this daily objective, you need to participate in the “Capture — Contend” mode. Go to the pause menu, choose “Online”, “Jobs”, “Play Job”, “Rockstar Created” (not necessary), “Capture”, and choose any job which name starts with “Contend” and where two players are enough.
To complete this objective as quickly as possible, set the end conditions as “Time Limit” and one round limit. Confirm settings and invite at least one player to the job. If no friends can help you at the moment, set the matchmaking option as open, run auto-invite, and wait for random players to join.
You can also try to find a capture using the Quick Job option or accept an invite (how to do that: Jobs in GTA Online). However, in this case, you will not know a type of capture in advance. To complete this daily objective, you need strictly Contend type.
The outcome of the capture doesn’t matter. The main thing is to complete the job because this daily objective completes after it’s ending. If other players quit the job, this will not affect you negatively.