What does it mean? "The people graviated with their drinks to the kichen"

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They all moved towards the kitchen.

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They moved towards the kitchen that they are attracted to. 
'Graviate to or towards somebody or something' is a phrasal verb meaning 'move towards somebody or something that you are attracted to'.

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I think you mean "gravitated."

"The people gravitated with their drinks to the kichen" -> They all gradually moved towards the kitchen.

Gravitate:

1. To move in response to the force of gravity.
2. To move downward.
3. To be attracted by or as if by an irresistible force: "My excuse must be that all Celts gravitate towards each other" (Oscar Wilde).

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Gravity and gravitation - that which attracts things to other things. :)

So the people had their drinks in hand, and all moved (gravitated) towards the kitchen.  Just like how the Earth's gravity can pull in a wayward comet to destroy us all.

Except these people probably enjoyed cake instead.

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