Anathema was originally a Greek word, ἀνάθημα (anathēma). In general English use, it has the basic meaning of "a curse". This used to be specifically in a religious sense, and was a serious penalty in the Church. Nowadays it is quite often used figuratively in non-religious contexts, to mean "a curse of any sort". A political leader, for example, may "pronounce anathemas" on individuals inside the party who have displeased him. This would be designed to stop others joining the person who has been anathematised - the verb that is linked to anathema.
Anathema is normally pronounced with the main stress on the second syllable. The vowels all have characteristic 'short' English sounds: 'an-ATH-er-ma', with the 'th' sound like that in 'THink', IPA: /ə 'næ θə mə/.
There is a much rarer meaning of anathema in church circles, "A thing devoted or consecrated to divine use" (OED). For this rare use - and only for this use - a pronunciation approximating to that in classical Greek is used - 'an-e-THEE-mer'. The third syllable has the stress, and a long '-ee-' sound, and the '-th-' is still the sound of 'THink', /,æ nə 'θiː mə/.
For a note on the plural, see anathemata.