I'm going to over-simplify this in order to avoid writing a novel on hypothesis testing.......
It's pretty much impossible to interpet the t-value without knowing the sample sizes in the study, unless the author directly provides the corresponding probability level for the t-value (usually referred to as a p-value).
But, very basically, the t-value is a statistic that indicates the size of an effect, from the standpoint of a bell curve (a probability distribution). The further away from 0, the more likely that the effect is "statistically significant" (another way of saying that the effect is not likely due to random chance - there is likely an underlying, repeatable cause).
For the overwhelming vast majority of situations, a t-value of 6.67 will be "statistically significant." In this specific situation, the researchers can comfortably conclude that the yoga class (assuming any other extraneous factors were well-controlled) was the underlying cause of the reduction in tension-anxiety scores.
Based on this, it appears that future similar studies would probably reveal the same basic outcome, and would make the yoga classes a viable, effective option in therapy.
The following link is a very good online resource that may help explain a lot of things:
Hope this helps clarify some things. Post back if you need further explanations....