I wouldn't put 'the' in front of patriarchy, as the parameters of patriarchy change over time, and 'the' suggests something static.
But generally, as I understand it, patriarchy is the name given to the fact that society, economy, politics, family, religion, the legal structure, you name it, has been organised, and is still organised, to benefit men. It used to be more overt, for example, in the fact that property and title went from father to son, that a wives property became her husband's, now it is more insiduous, the sexual objectification of women, the pay gap, the gendered nature of sexual and domestic violence, and so on.
Also, patriarchy benefits some men more than others, depending on age, race, class and sexuality, but generally, you would find that it benefitted a men of that group more than a woman of that group, iyswim.