The Goat as a Christian Symbol represents oppressors, wicked men and demonic forces. The goat also symbolises unrepentant sinners who will be separated from God on judgment day which is associated with the following Bible verse:
Matt. 25:31 "When the Son of Man comes in his glory, and all the angels with him, he will sit on his throne in heavenly glory. 32 All the nations will be gathered before him, and he will separate the people one from another as a shepherd separates the sheep from the goats. 33 He will put the sheep on his right and the goats on his left.
The Easton Bible Dictionary provides the following definition, meaning and emblem for the Goat Christian Symbol in the Bible.
1.) Heb. 'ez, the she-goat (Gen. 15:9; 30:35; 31:38). This Hebrew word is also used for the he-goat (Ex. 12:5; Lev. 4:23; Num. 28:15), and to denote a kid (Gen. 38:17, 20). Hence it may be regarded as the generic name of the animal as domesticated. It literally means "strength," and points to the superior strength of the goat as compared with the sheep.
(2.) Heb. 'attud, only in plural; rendered "rams" (Gen. 31:10,12); he-goats (Num. 7:17-88; Isa. 1:11); goats (Deut. 32:14; Ps. 50:13). They were used in sacrifice (Ps. 66:15). This word is used metaphorically for princes or chiefs in Isa. 14:9, and in Zech. 10:3 as leaders. (Comp. Jer. 50:8.)
(3.) Heb. gedi, properly a kid. Its flesh was a delicacy among the Hebrews (Gen. 27:9, 14, 17; Judg. 6:19).
(4.) Heb. sa'ir, meaning the "shaggy," a hairy goat, a he-goat (2 Chr. 29:23); "a goat" (Lev. 4:24); "satyr" (Isa. 13:21); "devils" (Lev. 17:7). It is the goat of the sin-offering (Lev. 9:3, 15; 10:16).
(5.) Heb. tsaphir, a he-goat of the goats (2 Chr. 29:21). In Dan. 8:5, 8 it is used as a symbol of the Macedonian empire.
(6.) Heb. tayish, a "striker" or "butter," meaning "he-goat" (Gen. 30:35; 32:14).
(7.) Heb. 'azazel (q.v.), the "scapegoat" (Lev. 16:8, 10,26).
(8.) There are two Hebrew words used to denote the undomesticated goat:, _Yael_, only in plural mountain goats (1 Sam. 24:2; Job 39:1; Ps.104:18). It is derived from a word meaning "to climb." It is the ibex, which abounded in the mountainous parts of Moab. And _'akko_, only in Deut. 14:5, the wild goat.
Goats are mentioned in the New Testament in Matt. 25:32,33; Heb. 9:12,13, 19; 10:4. They represent oppressors and wicked men (Ezek. 34:17; 39:18; Matt. 25:33).
Several varieties of the goat were familiar to the Hebrews. They had an important place in their rural economy on account of the milk they afforded and the excellence of the flesh of the kid. They formed an important part of pastoral wealth (Gen. 31:10, 12;32:14; 1 Sam. 25:2).