In many societies the firstborn child enjoys special privileges and responsibilities.
In Israel the firstborn (oldest son) received a double inheritance of every other son and a special blessing as his birthright (Deut 21:17). Esau didn’t value his birthright and sold it to Jacob for a meal, later sorely regretting it (Gen 25:29-34, 27:34).
From the time of the Exodus the firstborn males (human and animal) were to be consecrated to God – the sons and some animals being redeemed (bought back by money) while other specific types of animals were sacrificed (Ex 13:2,12-16, 22:29,30, 34:19,20; Num 18:15,16).
In the absence of the father, the firstborn son had authority over his siblings. Female humans were seldom given any recognition or status in society until towards the end of the NT.
Christ was the firstborn of His mother (Lk 2:7). He also is the firstborn Son (among many redeemed Christians) of His heavenly Father so is in the position of honour and authority over us (Rom 8:29; Col 1:18; Heb 12:23; Rev 1:5).