Twixt simply means 'between'. It is an old, shortened form of 'betwixt', and it survives now only in poetry, in old sayings, and in writing that wants to sound old-fashioned or grand. You will see it written 'twixt' with an apostrophe, showing the missing front of the word. Nobody uses it in ordinary speech; if you said it in a shop, people would think you were joking. Where you do meet it is in fixed phrases — 'twixt heaven and earth', 'twixt the cup and the lip' — and in the names of shops, pubs and songs, where the old sound is the whole point. Read it as 'between' and you will always be right.