Old Cheddar means “aged cheddar.”
There is no standard definition of what constitutes “old”, given that Cheddar is made in many different countries under many different jurisdictions. The only thing you can count on is that the Cheddar labelled “Old” is “more aged” than other pieces of Cheddar in a cheese manufacturers’ line up.
In practice, the aging can be anywhere from a year to 10 years or more, though some that are labelled “old” don’t seem to have even come near their first birthday.
Old Cheddar can be yellow or white.
North American recipes often call for Old Cheddar, because the writers of the recipe want the flavour of the cheese to come through. With most North American cheddar, buying Old Cheddar is the best hope you have of getting any taste at all out of it.