Maximum bidding is setting your bid to the max allowed bid by the individual pay per click search engine.
This is not suggested for almost any keyword. There are very few instances when this is a worthwhile technique.

If you are the first one to use this bidding technique, you will always be number one for a term, however, if you are not prepared to pay $50-$100 per click, do not use this strategy as someone will price pin you and make you pay for it.

This strategy is good for conversions that are worth millions of dollars. Often you will see words that result in class action lawsuits, and other such large settlements bid for at this rate. Outside of some very specific instances, this bidding strategy should never be used.