Current flows from the positive to the negative end of a battery or power supply. This is how it is written, described and measured. So, for example, if you are calculating the magnetic field caused by a current - the direction of the current is in the positive to negative direction. In other words, in your example, the current flows from the red (or yellow) wire through the load, and into the black.
If you go beyond the concept of bulk flow in the wire, and look at how the actual current is carried, then things become more complicated. In metal, the electrical current is carried by electrons. Electrons have a negative charge, and so the physical direction that the electrons move in must be opposite to the direction of the current flow.
Electrical current isn't always carried by electrons. If you pass an electrical current through a substance like molten salt (sodium chloride), then half of the current is carried by positively charged sodium ions. These flow in the conventional current direction - from positive to negative - and congregate at the negative electrode where they pick up electrons from the electrode and form sodium metal (and this is how metallic sodium is produced). The negative chloride ions carry the other half of the current, and flow in the reverse direction (same as electrons) from negative to positive (where they dispose of their excess electrons to the electrode and form chlorine gas).