The most common form of hypothyroidism is autoimmune primary hypothyroidism (Hashimoto's). This is when an autoimmune response attacks the thyroid gland which gradually fails. The pituitary puts out a hormone TSH which stimulates the thyroid to produce thyroxine (T4) and a little triiodothyronine (T3 - called 'liothyronine' in tablet form). The body converts the T4 to T3 as and when it needs it. T3 and T4 are mostly bound to transport proteins but a small fraction are unbound or 'free'. It is these free hormones 'fT3' and 'fT4' that are relevant.
The pituitary detects the fT3 and fT4 in the blood and as these levels falls it releases TSH, TSH rises dramatically as fT3 and fT4 fall. Thus, TSH is considered a sensitive marker of an individual's thyroid hormone status. This is true, but in some cases other conditions can reduce the pituitary output and the TSH assay is not always reliable.
The thyroid function test usually measures TSH, fT3 and fT4 (usually a GP can't get the fT3 assay done). If your thyroid gland is failing the TSH will be high and fT4 will be low. If the antibodies are high this shows you have autoimmune thyroid disease which is very common.
When you see your doctor ask for a copy of the blood test results. More important describe your symptoms and how they affect your life. Ultimately, if you have signs and symptoms of hypothyroidism it is important to ask for a trial of levothyroxine. The signs and symptoms are more important than the blood tests, unfortunately doctors tend to give too much weight to the blood tests.