1.
if you are in favour of sb/sth, you support and agree with them / it :
He argued in favour of a strike.
There were 247 votes in favour (of the motion) and 152 against.
I'm all in favour of (= completely support) equal pay for equal work.
Most of the 'don't knows' in the opinion polls came down in favour of (= eventually chose to support) the Democrats.
2.
in exchange for another thing (because the other thing is better or you want it more) :
He abandoned teaching in favour of a career as a musician.