It was required of Christ as it is required of all men, taught Nephi, that he follow the strait and narrow path (2 Nephi 31:9). A straight path is one without deviation, whereas a strait path as spoken of in this text, is one that is strict, narrow, and rigorous. Both expressions are appropriate descriptions of the path that leads to the presence of God.
In this instance, however, the emphasis is on the strictness with which all who would be saved must comply with the ordinances of salvation. Salvation is found only in willing obedience to the Father, never in neglect, disobedience, or the pursuit of one's own will. As it was, it was necessary for Christ to be obedient in all things to work out his salvation. It is necessary for all men to do the same.