"Old" means that some Bitcoins are at one address for a long time.
For example, from the aspect of AML risk score, "older" Bitcoins always have a very low risk score and are easier to accept in most services.
~snip~
If you have coins that can be linked to anything that is otherwise considered problematic, then it doesn't really matter whether they are coins that someone has been keeping in their wallet for 6 days or 6 years. For example, if you try to check the AML score of coins you got in a mixer campaign 5 or more years ago, believe me, they didn't clear on their own if you haven't moved them since then.