The letter ת represents the phoneme /t/. In Modern Israeli Hebrew, this phoneme is pronounced [t] (like the <t> in English tap).
In the Masoretic Text, the letter ת takes a dagesh (תּ) not only when geminated, but also at the start of a word or after a consonant. In Ashkenazi Hebrew, it is pronounced [t] when it has a dagesh, and [s] (like the <s> in English see) in other cases. In Yemenite Hebrew, it is pronounced [t] when it has a dagesh, and [θ] (like the <th> in English thick) in other cases; it is commonly believed that the same was true in Classical Hebrew.
In Modern Israeli Hebrew, the sound /θ/ (like the <th> in English path), which occurs in various foreign phrases and proper nouns, is commonly written ת׳(th).
Nouns ending in ת tend to be feminine, and many adjectives and participles form their feminine singular forms by appending ת to the masculine singular form (plus vowel changes). This is a reflex of Proto-Afroasiatic.
In many cases ת alternates with silent ה in different forms of a verb or noun; for example, feminine nouns whose singular indefinite forms end in ה tend to have singular construct forms ending in ת. (In many cases, this results from an original etymological /t/ having been lost in certain word-final contexts.)
For information about ת as a sort of prefix in various future-tense (prefix conjugation) forms, see Appendix:Hebrew verbs.
For information about ת as a sort of suffix in second-person singular past-tense (suffix conjugation) forms, see Appendix:Hebrew verbs.