Great question, Loretta.  I'm sure you will get many different
interpretations of what the passage in Hebrews means and I wouldn't get into
the fray of providing an answer if you hadn't asked for what it means to me
personally.  So, not trying to be dogmatic or refute anyone else's
interpretation, I want to share what I believe the passage is conveying to
those who have ears to hear, based on personally experiencing that rest.
    In my own life, as a minister, I worked hard and did everything that I
knew to glorify God and bring others to a saving knowledge of Jesus Christ.
It truly seemed a laborious task until one day, the Holy Spirit began to
show me that indeed there remained a rest into which I could enter but had
not yet done so.  In that rest, I could rest from my labors and rely on him
to do the labor.  Since He is so much more powerful than myself, I could
accomplish much more by entering into his rest than I could through my own
labors.  Israel did not enter into their rest because of unbelief and that
along with lack of knowledge prevents most of the church from entering into
the rest that God has for his children.  If you will have it, Isaiah
28:11-12, gives us the key to understanding that the rest is the baptism of
the Holy Spirit.  It is the rest and the refreshing wherewith the weary may
rest.
    Not only can I witness to the great rest that came through receiving the
Holy Spirit in my own life, the presence of the Holy Spirit has opened up a
whole new dimension and relationship with my Heavenly Father.  American
Express says, "don't leave home without it" and that is exactly what Jesus
told his disciples, "but wait for the promise of the Father, which, saith
he, ye have heard of me.  For John truly baptized with water; but ye shall
be baptized with the Holy Ghost not many days hence."  Peter on the day of
Pentecost boldly proclaimed to the Jews that "the promise is unto you, and
to your children, and to all that are afar off".  The promised rest left us
in Hebrews 4:1 is that same promise that Jesus and Peter spoke of in Acts,
which was prophesied in Joel 2:28-29, "And it shall come to pass afterward,
that I will pour out my spirit upon all flesh; and your sons and your
daughters shall prophesy, your old men shall dream dreams, your young men
shall see visions:  And also upon the servants and upon the handmaids in
those days will I pour out my spirit."
    Just as Israel in Moses day looked for a promised land, but did not
enter into it because of unbelief, the majority of the Jews of Jesus day did
not enter into their rest either because they stumbled at the stumbling
block due to unbelief.  The Jesus in Heb. 4:8 is actually Joshua, who did
enter into the promised land, but it was only a type of rest and not the
true rest, because David later in Psalms 95 implies that the rest is still
unfulfilled.  Then in verse 11 the Hebrews (and us) are exhorted to strive
to enter into that rest still available and not fail after their example of
unbelief.  To me, the rest spoken of here, that is so important for the
church to enter into, is the baptism of the Holy Spirit.  The experience
immediately changed my emphasis from striving to labor, to just obediently
relying on him and following where he leads.  Zechariah 4:6 describes the
contrast as, "Not by might, nor by power, but by my spirit, saith the LORD
of hosts."
    Now, this rest is not an option, but is just as much a necessity to us
as entering the promised land was to Israel.  Chapters 1 & 2 of Hebrews
declare the supremacy of Jesus to all others and yet he was made like unto
his brethren to bear our sins, provide reconciliation with the Father, and
become our merciful and faithful high priest.  Notice that the Hebrew
audience in 3:1 are also partakers of this heavenly calling, so he is
addressing saved believers and the rest, by implication, can't be salvation.
You might ask, "If it's not salvation, then what is there to fear about not
entering in?"  Another good question, I'm glad you asked.
    It appears that the rest (baptism of the Holy Spirit) is a requirement
to be part of the Bride of Christ.  As such, when there is a partial rapture
(first fruits rapture) of the church which only includes those who are
clothed in righteousness with oil in their vessels, this passage will become
perfectly clear to those who are left behind.  How sad it will be when those
that remain, realize that they could have enjoyed the rest all along (4:10),
but instead of fearing to come short of the promise (4:1), and taking
earnest heed to the things which they had heard (2:1), they let them slip
and do not escape (the tribulation) because of neglecting so great a
salvation (2:3).  Yes, as Isaiah 28:10 said, it is here a little and there a
little, but it's all there for those who will allow the Holy Spirit to
quicken it to them.
    I'm not trying to put fear into anyone, but this passage is exhorting us
to fear coming short of this promise, because the consequences of neglecting
it may be more drastic than the consequences of Israel's unbelief.

Be not drunk with wine, wherein is excess; but be filled with the Spirit;

David  Robinson