Here is a link to an article that goes over the basics of the two most common types of testers, emission and mutual conductance (aka transconductance).
http://www.tungsol.com/html/faqs7.html
Emission testers basically operate the tube as a diode and give a measurement of the emissive capabilities of the cathode, the result is given as a percentage, with 100% being considered NOS. This is the most basic type of tester and gives some idea of remaining tube lifespan. However, it doesn't tell you much about the actual operating conditions of the tube.
A more advanced type of tester is a mutual conductance tester, the likes of a Hickok. These types of testers measure mutual conductance of the tube at a specific operating point. Mutual conductance (gm) is one of the three tube constants, the others being amplification factor (mu), and plate resistance (rp). They are related by the equation mu = gm x rp. The amplification factor (mu) is what is going to affect the practical voltage gain of the tube. If mu for two sections of a tube or two different channels of an amplifier differs significantly, you may hear a channel imbalance. But these testers do not measure mu, they measure gm. By the equation, they are directly proportional assuming rp is constant (it isn't, but close enough to be assumed). So basically you can infer that mu will be at its proper specification if gm is too, that's the idea at least, reality is different but good enough to be practical.
Gm testers will either give a direct value for gm (2600 micromhos for the 6SN7, for instance) OR they will give a value based on a normalized scale created by the tester manufacturer. For example, the Hickok TV-7D/U has its own gm scale and gives a value based on that scale that must be compared to the reference value given in the tester manual.
Okay, so for emission testers, you will see the test result as a percentage. For gm testers, you will see either A) a direct value of gm in micromhos that must be compared to the reference value from the tube datasheet or B) a value based on the normalized scale for that specific tester. For B, the seller will often say what the minimum reference value is for that tester, which is often considered to be 60% of a NOS value. So they might say something like "tested 64 on a calibrated Hickok TV-7D/U with 45 being minimum", or they might just say "tested 64/45 on a calibrated Hickok TV-7D/U". If 45 is the 60% of NOS gm based on the Hickok scale, some simple math would tell you that 64 would be roughly 85% of a NOS gm value.
That's the basic idea. However some sellers will use backslashes when tubes have two different sections, like a 6SN7. They might write it as "2700/2600 with 2600 being NOS" or "66/68 with 45 being minimum" in the case of gm testers with normalized scales, so watch out for that.
One more thing, the units of transconductance. By Ohm's low, Ohm = V/A. The units of the mutual conductance, A/V, are the inverse, the reason it is written as mho (yeah, it's literally just ohm backwards). So a millimho is mA/V, a micromho is μA/V. Transconductance of solid state components is much higher these days, and everything is expressed in Siemens (S) which is equivalent to mhos (A/V).
So, 1S = 1mho = 1 A/V = 1,000 mA/V = 1,000,000 μA/V = 1,000,000 micromhos.
That is the crash course.