Bitachon is an example of a Biblical Hebrew word that took on a very different set of meanings with the rise of a modern, Hebrew-speaking country.
The root batach literally means to lean or rest on someone or something. Batach b' means "to trust in", usually in God, when used by the Bible, eg: "It is better to trust in God than to trust in any man" (Psalms 118:9) or "I have placed my trust in Your lovingkindness."
From this, bitachon comes to mean faith and is often used interchangeably with emunah. But it means faith in an active sense, consciously placing the burden or one's concerns and worries on God and trusting that things will work out.
The core of the secular Zionist revolution was to shift the Jewish consciousness of what we should be relying and trusting in, from God to ourselves. Bitachon now is the exhaustive series of security checks one passes through before boarding an El AL flight and, in Israel, before entering a shopping mall, café or post office.
