In the context of performing a Search Engine query, a Broad Match query is simply a query phrase which does not have quotation marks (") around it.
Such a query does not require the webpages returned by the query to contain the exact phrase you typed in. In other words, it is a proximity-based search. This is in contrast to a phrase match query, which does require the webpages returned to contain the exact phrased queried. In the context of placing an Ad in Google AdWords, Broad Match is the default AdWords option.
If you include general keyword or keyword phrases, such as tennis shoes, in your keyword list, your ads may appear when users search for tennis and shoes, in any order, and possibly along with other terms. For example, your ad may appear for the queries buy tennis shoes and tennis sneakers but not tennis players. Broad match ads may also appear on relevant variations of your keyword phrases and plurals, as well as some related keywords and phrases via Google's expanded keyword matching technology. Broad matches are often less targeted than exact or phrase matches. If you decide to use broad-matched keywords, we recommend you create keyword phrases containing at least two descriptive words each. A note about expanded matching: The AdWords system continually monitors system-wide keyword performance and other relevance factors. This helps determine which expanded matches and variations are the most relevant to their searches.