"Tone" here refers to tonus or tonic activity. Wikipedia says:
Tonic in physiology refers to a physiological response which is slow and may be graded. This term is typically used in opposition to a fast response.
I'd go a step further, and say that "tonic" or "tone" to a neurophysiologist is often synonymous with activity that is so slow that it's the baseline, in contrast to phasic responses which are evoked by some sort of stimulus.
When someone says "increased vagal tone" they mean "there are more action potentials being fired in axons in the vagal nerve when the person recording the activity isn't doing anything to produce/evoke/stimulate it". This is more of an observational quality than anything specific; it doesn't say which particular fibers are active, or whether activity is increased in all fibers a little or in a few a lot. However, vagal tone is often not measured directly, instead it's measured by vagal effects on the heart rate:
In most cases, vagal tone is not measured directly. Instead the processes affected by the vagus nerve – specifically heart rate and heart rate variability – are measured and used as a surrogate for vagal tone. Increased vagal tone (and thus vagal action) is generally associated with a lower heart rate and increased heart rate variability.
So, you're right, when someone tells you "increased vagal tone", the next question you should ask them: "What is meant by increased vagal tone? How did you measure it?" - otherwise you don't know for sure what they mean. If they can't tell you, then possibly they don't know what they're talking about.
