T test signifigance, what does my value actually mean

Okay so here is the deal, I have computed a full t-test comparison of data but I have no idea what my final value actually represents. Here is the details: I have 68 Degrees of freedom, and a t value of 1.761 and I can see my calculated t value is under that of the 0.5 value on the t chart but what does that mean? I need to understand what it means or I'll never remember anything about this.

Thanks

Somewhat difficult to answer since there are a few different ways to set up a t-test so the interpretation of what the result means depends on what type of t-test it was.

The explanations for some different kinds of t-test are in this Wikipedia section:
Student's t-test: Uses
Student's t-test: Assumptions
http://en.wikipedia.org/wiki/Student%27s…

If it is a one-sample t-test then typically you are testing if the mean matches a particular value. If the actual mean is much larger or smaller, then the calculation gives a larger number in both cases (since it has squared terms in the numerator). Then if your t value is too big you conclude the actual mean is different (reject the null hypothesis) or if your t value is small you conclude the actual mean is not shown to be different (accept the null hypothesis).

It means there is only 50 % chance that this difference can come by chance.