Entering in at the strait gate

What do the Mormon scriptures say about entering in at the strait gate?

How do Latter-day Saints understand the parable of entering in the strait gate?

The context is described more in Luke 13:23-30 than in Matthew's chapter 7.

"Then said one unto him, Lord, are there few that be saved? And he said unto them, Strive 
to enter in at the strait gate: for many, I say unto you, will seek to enter in, and shall not 
be able. When once the master of the house is risen up, and hath shut to the door, and 
ye begin to stand without, and to knock at the door, saying, Lord, Lord, open unto us; and 
he shall answer and say unto you, I know you not whence ye are: Then shall ye begin to 
say, We have eaten and drunk in thy presence, and thou hast taught in our streets. But 
he shall say, I tell you, I know you not whence ye are; depart from me, all ye workers of 
iniquity. There shall be weeping and gnashing of teeth, when ye shall see Abraham, and
Isaac, and Jacob, and all the prophets, in the kingdom of God, and you yourselves thrust 
out. And they shall come from the east, and from the west, and from the north, and from 
the south, and shall sit down in the kingdom of God. And, behold, there are last which 
shall be first, and there are first which shall be last."

This is how I see it when I read the following Mormon scriptures:

"Enter ye in at the strait gate; for wide is the gate, and broad is the way, which leadeth 
to destruction, and many there be who go in thereat" (3 Nephi 14:13).

The broad way leads to destruction.

"And the mists of darkness are the temptations of the devil, which blindeth the eyes, 
and hardeneth the hearts of the children of men, and leadeth them away into broad 
roads, that they perish and are lost" (1 Nephi 12:17).

The devil leads one into the broad roads, away from the strait gate.

"And it came to pass that when Jesus had ended these sayings he said unto his 
disciples: Enter ye in at the strait gate; for strait is the gate, and narrow is the way 
that leads to life, and few there be that find it; but wide is the gate, and broad the 
way which leads to death, and many there be that travel therein, until the night 
cometh, wherein no man can work" (3 Nephi 27:33).

The strait gate leads to life.

But what type of life?

"O then, my beloved brethren, repent ye, and enter in at the strait gate, and continue 
in the way which is narrow, until ye shall obtain eternal life " (Jacob 6:11).

The strait gate leads to eternal life. The broad way leads to destruction as seen earlier.

"For strait is the gate, and narrow the way that leadeth unto the exaltation and 
continuation of the lives, and few there be that find it, because ye receive me not in 
the world neither do ye know me" (D&C 132:22).

The strait gate leads to eternal life (exaltation), which is becoming a god.

Those who do not reach exaltation are thrust out, destroyed so to speak, where they 
experience gnashing of teeth.

Is this the way you see it?

See the section "Who is saved? Should Latter-day Saints be afraid?" in the 
What is salvation? page.