two pronunciations: ðə before a consonant, and ði before a vowel.
The sound ð is often deictic. That means it points to something in the world (or something that's been pointed out earlier in the course of discussion). (digit - doigt - deixis)
e.g. there, them, they, then, this, that, thus, therefore, these, those, thither, whither, etc.
Another way of saying 'definite article', which I personally find more useful. People use determiners to determine just what exactly they are talking about:
- his cat
- a stray cat
- any cat
- all cats
- no cats
- that fat cat
- these kittens
- those mice
- them (nb: not a determiner)
- The more, the merrier...
- The longer I waited to go to the hospital, the worse it got...