Thanks in advance
Functionalism believes that in society, everyone serves a 'function' or purpose. It's usually described akin to a machine, where every person works as a cog in the machine to keep it running. In the same way that every person serves a purpose to keep society running.
Traditional functionalism saw the man as the 'breadwinner' the function of the man was to work and earn money to keep both society and his family afloat. The woman would be the 'warm bath' she would be there to emotionally support the family and raise the children, teaching them the norms and values of society as well as providing emotional support to the breadwinner to keep them motivated and happy.
Marxism is more the 'doom and gloom' side of the coin, and runs off of the idea of Capitalism. It says there's a clear class divide; you have the bourgeoisie (the upper classes) that own the means of production and hold the power. They use this power in order to exploit the Proletariat (the working class) for their hard work and labour. It claims that the working class are oppressed by the upper classes, and that children are merely raised to become the 'next generation of workers'. Marxist feminists claim that working-class women are the most oppressed in society, as they provide both working labour but also free labour in the household (the cooking, cleaning, babysitting etc).
Hope this helps!