If X can be matched with Y the goal succeeds else the goal fails. A X=Y goal will consider an uninstantiated variable to be equal to anything. A X=Y goal will always succeed if either argument is uninstantiated.
Examples
?- a=a.
yes
?- a=b.
no
?- a=X.
X = a
yes
?- 2=1+1.
no
?- p(b,c)=p(b,d).
no
?- p(b,c)=p(c,b).
no
?- p(b,c)=p(b,X).
X = c
yes
?- p(Y,c)=p(b,X).
X = c
Y = b
yes
?- [a,b,c]=[a,b,c].
yes
?- [a,b,c]=[a,b,d].
no
?- [a,b,c]=[X|Y].
X = a
Y = [b,c]
yes
?- [X|[b]]=[a,b].
X = a
yes
?- [a,b,c|X]=[a,b,c,d,e,f,g].
X = [d,e,f,g]
yes
?- [a,b,c]=[a,b,c|[]].
yes
?- [a,b,c]=[X|[]].
no