The Standards for Mathematical Practice are informed by two important resources:
the National Council of Teachers of Mathematics (NCTM) process standards and
the National Research Council’s (NRC) report Adding it Up Adding: Helping Children Learn Mathematics.
The five NCTM process standards highlight ways of acquiring and applying content knowledge:

problem solving

reasoning and proof

communication

representation

connections
Additionally, the NRC report describes five strands of mathematical proficiency:

conceptual understanding  comprehension of mathematical concepts, operations, and relations

procedural fluency skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

strategic competence ability to formulate, represent, and solve mathematical problems

adaptive reasoning capacity for logical thought, reflection, explanation, and justification

productive disposition habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
The NRC report stresses that the strands are interwoven and interdependent in the development of proficiency in mathematics. These strands provide a framework for discussing the knowledge, skills, abilities, and beliefs that constitute mathematical proficiency.