In the Alter Rebbe’s siddur, Torah Ohr, in his introduction to Tikkun Chatzos, defines yirei boshes as follows:

Yirei boshes is for example, the internal feeling of shame one feels in the presence of  a great man in one’s generation, a tzaddik, etc. The fear is from motivated from within himself: this is called yira ilaa, to become shy in the presence of the Light of the Endless One Boruch Hu, who integrates Himself into the Chochma of Atzilus… before this great Light all existence is as nothing.