Purpose of crew members
The only real reason to have crew members is so that they can fight battles with you. To fire a cannon, you'll need two crew members.
They demands things in return for their services. They become less happy when they do boring stuff, like working, losing battles and traveling the great Caribbean Sea. When they are angry they will refuse to work / fight for you.
In order to fix this you have to please them, with food and drinks. You can visit the tavern and buy them some wine perhaps, or give them rum from your goods if you have any.
You are also responsible for their health. If they lose to much health they will die in battle. You can give them medicine after battles, or visit the towns healer when you are in land again.
Getting more crew members
When you win battles at sea some of their crew will offer to join you. You can then choose how many of them you want to accept. The other method is to visit the tavern and speak to the sailors there, they often want to offer their services for free. You could also visit the slave market, but it's expansive!
Get to know them
If you check your inventory you will get unnecessary amounts of information about your crew. All of them are separate beings, with their own name and description. You can also see for how long they have been with you, how much money they have gained of being your crew.