In federalist 10, the factions james madison refers to would most likely be

James Madison's apprehensions about factions focused especially on the role of money and property in creating competing groups in society based on their wealth or property holdings. Landholders could be such a faction. Banking and moneylending agencies could be such a faction. They might work their will against the majority of the people. At the same time, factions could develop among the less wealthy majority of the people that would seek to strip away rights and property from the wealthiest citizens to redistribute it to those less well-off.

Madison argued that factions of any kind war against the unity of the republic. Factions consider only their own position, rather than the rights and well-being of the whole community or nation.