The Hebrew Christians were struggling and were ready to 'throw in the towel'. The persecutions were too much, the slander was too much, the difficulties of maintaining their profession of faith was too much.
The author of Hebrews (lets call him Paul), comes along and he says, 'brothers, sisters, hold fast your profession,' meaning hold it tightly. Do not allow it to be let go of.
Commenting on Paul's words to the Hebrews, John Owen writes, "Their [The Hebrew Christians] faith, their love, their diligence, were decayed; and they performed not the works they had some time been fruitful in. And in all these things are men liable to let go their profession. Again, growth and progress in all these is required of professors. The kingdom of God is a growing thing, and out to be so in all them in whom it is by its grace, and who are in it by the observation of its laws."