As its name implies, Minimalism is a reduction of form to its absolute essentials. Stylistically, Minimalism is stark simplicity. It was influenced by Japanese, de Stijl, and the International Style. There's an emphasis on rectilinear lines.
Minimalist artists of the 1960s were reacting against what they thought was an excessive extension of the artist's personality in the works of abstract expressionists. Their approach was to make art non-representational, neutral in color, geometric, and stripped of traces of motion or meaning.
A great example of this is Tony Smith's Die:
It's a six by six-foot cube of steel. Its dimensions were supposedly based on the human body a la Da Vinci's Vitruvian Man. It demonstrates a balance in which the work of art is smaller than a monument but larger than what would be considered a simple object. It was intended to be interacted with, in that viewers can move around it and touch it, and as a reference point by which viewers can experience themselves and their surroundings by the relativity to the sculpture.
It's important to reiterate that the idea behind Minimalist art is quite often essential to understanding it. Minimalism's influence on architecture or in Scandinavian furniture design, for example, results in buildings and objects that can be appreciated for their simplicity and adherence to form following function, which is an idea that found traction with the International Style in architecture. Art for appreciation doesn't have that functional quality to it.
Donald Judd's Concrete Blocks, like Smith's Die sculpture, undermine the myth, in their view, of artistic originality by the fact that they contracted foundries to produce these works, rather than create them themselves.
One of Judd's Concrete Blocks:
For Judd's blocks, their location is important as well, as they reflect the starkness of the Marfa, Texas countryside. So to move the objects from their location would be to change their meaning. This idea of concept and experience is very important within Minimalistic art.
Within Judd's and Carl Andre's (pictured below) work, there's also an idea of seriality, or repetition of form, in which the importance of each discrete element is made manifest by its relationship to the corresponding parts.
They're arranged in such a way that they're collectively significant but independently meaningless. The ratio and repetitive harmony of this artwork only work because it contains exactly the right number of elements, and each element is the correct size. To lose one would result in a complete lack of cohesion.
Source: This work is adapted from Sophia author Ian McConnell