T-scores are standard scores obtained by setting the mean at 50 and the standard deviation at 10, so that for instance a T-score of 30 denotes a score two standard deviations below the mean. A typical application of T-scores lies in multi-scale personality tests, where T-scores serve to make comparison between the scales possible.
Often, T-scores are not based on the actual raw score mean and standard deviation (that would be linear T-scores), but are normalized standard scores; that is, the raw scores are first converted to quantiles (like centiles), which are then converted to z-scores via the normal distribution. These normalized z-scores are then multiplied by 10 and added to 50 to arrive at the normalized T-scores. Whether linear or normalized T-scores should be used depends on the raw score distribution; if strongly skewed, normalized T-scores are considered the better choice.
In general, one should make certain to understand the difference between linear and normalized standard scores of any kind.