Nakama (なかま) means the people you share a group or a goal with: teammates, crewmates, comrades — “my people”.
In a team anime the word is everywhere. The crew sets sail, the club enters the tournament, and someone declares that these are their なかま. Subtitles try “friends”, “comrades” or “crew”, and each one catches only part of it.
What it actually means
なかま is someone in the same circle as you: the same team, club, class, workplace or hobby. What joins you is the thing you do together, not how close you feel. You can have なかま you hardly know, and close friends who are not your なかま in anything.
なかま or ともだち?
ともだち is a friend: someone you like spending time with. なかま is someone on your side in something. Your football team are your なかま; the person you call on a bad day is your ともだち. Often the same person is both.
わたしも なかまに いれて ください！
Please let me join you too!
もちろん！ いっしょに しましょう。
Of course! Let's do it together.
Can you use it?
Yes — it is an everyday word, not anime slang. People talk about しごとの なかま (people they work with), the なかま in their band, or the なかま they go hiking with. The anime version is simply the same word said with a lot more feeling.
One related word you will hear: なかまはずれ, being left out of the group — the opposite of everything なかま stands for.