This has been described as possibly the most misquoted part of the AA Big Book. It's usually offered as a justification for using our God-given intellectual powers to get something done -- generally something that we want.

In fact, in its context the phrase means almost the complete opposite.

It is preceded by the statement, We ask God to direct our thinking, especially that it be divorced from self-pity, dishonest or self-seeking motives. Under these conditions we can employ our mental faculties with assurance .... And immediately afterwards, it says, Our thought-life will be placed on a much higher plane when our thinking is cleared of wrong motives.

In other words, it's all right to use our brains as long as we're using them for something other than selfish motives. Otherwise, it's not all right. This is yet another example of the emphasis in the last three Steps on the abandoning of our personal agendas and seeking only God's will.