This means that the current that is passing through the tube at the particular settings in use is greater than usually expected. This tells you that you have a strong tube, relative to others of the given type.
There are many makes of, for instance, the 6L6 power pentode, from the originals back in the late 1930‘s to Czech, Chinese and Russian types today. There’s no real standard for what is a “6L6”. Some are stronger and some are weaker, even brand-new. A worn-out Wing-C is going to be stronger than an original RCA. This is why we don’t offer pass/fail standards for tubes, because it’s hard to say what is good and what isn’t good.