In Metal Gear Solid V, there are a total of 157 Side-Ops to complete. Not all of them are available from the very beginning of the game. After you complete several initial missions, you gain access to the first 2-3 side missions. More and more optional assignments become available as a result of your progress into the main storyline, or thanks to the side missions available at a given moment.
The majority of side missions only have a single primary objective. They may require you to, e.g. free a prisoner, capture an enemy officer or find blueprints for a rare item. In theory, you can play side missions while playing the main ones, but it is more convenient to complete them in-between the individual main missions (free roaming around the map).
Note - You can replay the selected side missions. However, you should do this only if you want to obtain more cash e.g. for your research (each side mission that you complete is usually rewarded with something between tens of thousands to hundreds of thousands of GMP).