What does it mean to carry out? - is that a food word like take out?

Yes, 'carry-out' is similar to 'take-out' for food. Usage can vary by region. I believe that in BrE, 'take-away' is commonly used. Perhaps someone British will confirm this.

Best wishes, Clive
Dear friends,

It is common for British people to have a «takeaway». It is often Chinese or Indian food.

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You can actually carry something (a bag etc...) out of a room, for instance. I'm not familiar to this being used in relationship to food, I would rather expect "carry away", as in "take away". But you can carry the dishes out of the kitchen and into the dining-room, or carry them outside, to the garden. The other native mods will correct me.

Then you can carry out a mission (for ex.), meaning you complete it. You can also carry out instructions, that is you do as you've been told.
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Dear friends,

May I be permitted to add, that it is common in a British café to be asked «Is it to eat in or to take away?».

In an American café, however, it has been asked, «Is it to eat in or take out?».

It is confusing. Emotion: smile

Kind regards, Emotion: smile