Yirat Shamayim, fear of Heaven, is a basic spiritual quality required in Judaism. Yirah means literally to fear, tremble or revere. Shamayim, meaning skies or heavens, is also a reference to God, as in English.
The Talmud (Shabbat 31a) likens someone who knows Torah but lacks yirat Shamayim to a palace treasurer who holds the inner keys to the treasure but does not have the outer key; ie what he has is useless.
Yirah, fear, is not generally thought of as a spiritual quality these days when self-confidence is all. The classic Jewish ethical writers, such as Rabbi Moshe Chaim Luzzatto (1707-47), stress the distinction between lower yirat Shamayim, the fear of punishment, (which certainly has its place in ethical training) and higher yirat Shamayim, which is to be suffused with awe and reverence for God and creation.
The Talmud also distinguishes between fearfulness or anxiety that ones spiritual life is not as it should be (often appropriate), and fearfulness about worldly matters, which in general is misplaced.
Everything is in the hands of Heaven, except for fear of Heaven, the Talmud famously states (Berachot 33a). Ultimately the only thing in the world that we control is our basic spiritual orientation towards the world.