What does eq_ref and ref types mean in MySQL explain

I’ll try an explanation…

eq_ref – imagine that you have two tables. Table A with columns (id, text) where id is a primary key. Table B with the same columns (id, text) where id is a primary key. Table A has the following data:

1, Hello 
2, How are

Table B has the following data:

1, world!
2, you?

Imagine eq_ref as JOIN between A and B:

select A.text, B.text where A.ID = B.ID

This JOIN is very fast because for each row scanned in table A there can be only ONE row in table B which satisfies the JOIN condition. One and no more than one. That is because B.id is UNIQUE.
Here you are: pseudo code which illustrates the processing at server side:

foreach (rowA in A)
{
    if (existsInBRowWithID(rowA.id)
    {
        addToResult(rowA.text, getRowInBWithID(rowA.id).text);
    }
}

ref – Now imagine another table C with columns (id, text) in which id an index but a non UNIQUE one. Table C has the following data:

1, John!
1, Jack!

Imagine ref as JOIN between A and C:

select A.text, C.text where A.ID = C.ID

Here you are: pseudo code illustrating the server side processing:

foreach (rowA in A)
{
    foreach (rowC in C)
    {
        if (rowA.id == rowC.id)
        {
            addToResult(rowA.text, rowC.text);
        }
    }
}

This JOIN is NOT as fast as the former one because for each row scanned in table A there are SEVERAL possible rows in table C which may satisfy the JOIN condition (nested loops). That is because C.ID is NOT UNIQUE.