Broad match keywords give Google the most freedom of what keywords will trigger your ads. Isaac's recommendation for new advertisers is to not use broad matches at all in the beginning, as Broad matches are soo loose.
Broad match modified - the search query needs to contain the modified terms for the ads to show in the query. So If the search in Google was 'buy ladies cap', then our ad for +women's +hats will not get shown.
Phrase match - gets shown as long as the whole phrase, in that exact order, is in the search query for the ads to show. But words can be prepended or appended to the phrase such as 'buy women's caps online'.
Exact match keywords must have the exact phrase and keywords and nothing else in the query to be shown. That is it only shows what's inside the bracket, in the exact order without any words prepended or appended to it. Google could however still show misspellings of the words in your exact phrase match.
Negative keywords - removing keywords for eligibility. For example, if I add free as a negative keyword then the ad will not get shown for the query 'free women's hats'.
Exact Match Negatives - such as -[men's hats] would only not show when the exact match is the entire query. So if the keyword was 'buy men's hats' the ads would still show.