To articulate the foot or leg is an instruction which comes to us from professional ballet and dance, but you may be more familiar with “articulated teddy bears”.
There are two kinds of teddy bears, the kind whose legs and arms and head have little joints inside, so you can move them to different positions, and the kind who are in a fixed (although somewhat flexible) position.
Articulation in the context of teddy bears and dancers is a physical expression of erudition. It means that they have and offer more subtle and fine-grain possibilities.
The application to tango dancers is that we need to learn to use more parts of the body independently and sequentially. During a step or while flying the legs, we are articulate the leg by moving the hip, knee, and ankle joints distinctly. We articulate the foot through the positions: flat, demi point, and point. This control enables us to create “natural” or “fluid” motion as well as stability.