Can someone explain what does "node* next" mean intuitively in that piece of code?

next is a pointer to the next item in the list, as the name implies.

Think of each struct instance (each node) as a piece of paper. You have a dozen pieces of paper, and you write a different number between 1 and 12 in the top right corner - this is the "address" of the node.
Now put them in a stack on your desk, and take the topone. Write the data on it and write "Next: 0" at the bottom right.
You now have a list with one element - the 0 is the next address, and there aren't any.

Take another piece off your stack, write different data on it, put "Next: 0" in the bottom right, and then change the "0" on the previous sheet to the number in the top right of the new one.
You now have a list with two nodes: the first one holds the address of the second in the bottom right corner, and the second says "there are no more" with a zero in the bottom right.

As you add new sheets, you repeat the process, replacing the last sheet "0" with the address of the new sheet, until you have a full list - and you can track through the list from the first sheet just by following the "chain" of next pointers.

Give it a try on your desk, and you'll see what I mean.

That's what

node* next;

means: next is a pointer to a node structure, and indicates the next item in the list.

struct node
{
  int data;
  node* next;
};

Such a code is typically used in linked list[^] implementation where a 'Node' contains some 'data' plus a pointer to the next 'Node':

 _______         ________
|       | next  |        | next
|data=5 | ----> |data=12 | ----> ...
|_______|       |________|