Between each node, an FEM solver chooses to assume the literal shape of the edges of each cell/element is either straight, or curved (aka first order or second order). When assuming either straightness or curvedness, the solver is said to be using linear or a quadratic shape functions. Cubic shape functions are rarely used. The shape functions are very basic linear and quadratic functions, that you can use in linear combinations to approximate basically any 1st order or 2nd order function. The solver calculates the shape of each edge between nodes as a linear combination of those shape functions. In other words, the shape functions are basis functions for describing the shapes of the edges.