There are three types of Keyword matching in Adwords:

Broad Match

Let's look at the difference between each one using the seed word 'chocolate'.

As the name suggests, a broad match for the keyword chocolate will be any search phrase that includes the word chocolate in any order including plurals, close variations and synonyms:

Phrase Match

If you set a single keyword to phrase match it will get the same results as above, but for multiple word phrases such as chocolate cake, you will get results that have the words in that order, eg:

Keywords set to phrase match will show with "quote marks"

Exact Match

This means your ad won't show unless the search types in exactly the same phrase in that order (but will include synonyms and close variants) .  These words will show with [square brackets].

Broad Match Modifier

Adding a + sign before a keyword phrase set to broad match will mean the search phrase has to include that word eg +chocolate cake +recipies.