What is a cell in the context of an interpreter or

Python code objects have an attribute co_cellvars. The documentation to PyPy's bytecode interpreter often uses the term Cell.

Among other langauges, Rust provides a Cell datatype. Googling suggests they relate to closures somehow.

What is a cell, in the context of a programming language implementation? What problem do cells solve?

In Python, cell objects are used to store the free variables of a closure.

Let's say you want a function that always returns a particular fraction of its argument. You can use a closure to achieve this:

def multiplier(n, d):
    """Return a function that multiplies its argument by n/d."""
    def multiply(x):
        """Multiply x by n/d."""
        return x * n / d
    return multiply

And here's how you can use it:

>>> two_thirds = multiplier(2, 3)
>>> two_thirds(7)
4.666666666666667

How does two_thirds remember the values of n and d? They aren't arguments to the multiply function that multiplier defined, they aren't local variables defined inside multiply, they aren't globals, and since multiplier has already terminated, its local variables no longer exist, right?

What happens is that when multiplier is compiled, the interpreter notices that multiply is going to want to use its local variables later, so it keeps a note of them:

>>> multiplier.__code__.co_cellvars
('d', 'n')

Then when multiplier is called, the value of those outer local variables is stored in the returned function's __closure__ attribute, as a tuple of cell objects:

>>> two_thirds.__closure__
(<cell at 0x7f7a81282678: int object at 0x88ef60>,
 <cell at 0x7f7a81282738: int object at 0x88ef40>)

... with their names in the __code__ object as co_freevars:

>>> two_thirds.__code__.co_freevars
('d', 'n')

You can get at the contents of the cells using their cell_contents attribute:

>>> {v: c.cell_contents for v, c in zip(
        two_thirds.__code__.co_freevars,
        two_thirds.__closure__
)}
{'d': 3, 'n': 2}

You can read more about closures and their implementation in the Python Enhancement Proposal which introduced them: PEP 227 — Statically Nested Scopes.