In commenting on James 5:7, Ellicott reminds us:
The early and latter rain.—It is, perhaps, just as well to recollect
there were only two seasons of rainfall in the Holy Land, and, if long
delayed, famine was a certain result. … The “early rain” fell during the
autumn sowing—in October, November, and December; “the latter” in
March and April.
Some versions translate these "early" and "latter" rains as "autumn" and "spring" rains respectively, eg, NIV and BSB, etc.
As to the significance of this agrarian simile, there is much debate, especially among some of the extreme Christian groups which I will avoid here. The simplest, most obvious explanation is that provided by Barnes who comments:
Behold, the husbandman waiteth for the precious fruit of the earth -
The farmer waits patiently for the grain to grow. It requires time to
mature the crop, and he does not become impatient. The idea seems to
be, that we should wait for things to develop themselves in their
proper season, and should not be impatient before that season arrives.
In due time we may expect the harvest to be ripened. We cannot hasten
it. We cannot control the rain, the sun, the season; and the farmer
therefore patiently waits until in the regular course of events he has
a harvest. So we cannot control and hasten the events which are in
God's own keeping; and we should patiently wait for the developments
of his will, and the arrangements of his providence, by which we may
obtain what we desire.
This idea of patience is suggested in the verse of James 5:7, itself, "Be patient, then, brothers and sisters, until the Lord's coming." In fact, the NLT makes this more explicit: "Dear brothers and sisters, be patient as you wait for the Lord’s return. Consider the farmers who patiently wait for the rains in the fall and in the spring. They eagerly look for the valuable harvest to ripen."
The "precious fruit" may well be an allusion to Gal 5:22, 23: "But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law." It might also include the mysterious workings of God sovereign providence in the affairs of men to finally resolve the problem of sin at His return, or "His coming" as James 5:7 says.
(I cannot see an immediate connection with Heb 6:11, except for the incidental use of the word "patient".)