The spin of an electron is like the daily rotation of the Earth. The magnetic quantum number is like the yearly revolution of the Earth around the Sun. Both carry angular momentum. This angular momentum is typically measured by applying a magnetic field, which is sensitive to rotation within one particular plane, or equivalently around one particular axis that is perpendicular to that plane - the "North-South" axis. If the electron in any way turns around the axis one way, as a moving charge it produces a magnetic field aligned with the external magnetic field, but if it turns the other way it will be opposite to that field. Increasing the total magnetic field in the region takes energy, which can be seen by spectroscopy as absorption of higher-frequency light. Electron spin resonance (ESR) will measure the energy difference when an electron flips the direction of its spin, while the Zeeman effect measures the difference between positive and negative magnetic quantum number.
Under ordinary circumstances where powerful magnetic fields are absent, the direction of an electron's spin is unknown (typically written as an up arrow in molecular orbital diagrams when it is unpaired), while the complex-valued solutions for electron density for + and - magnetic quantum numbers are added together to represent the real-valued standing wave produced by these two electrons. That standing wave is the lobed p, d, or f orbital depending on the absolute value of the magnetic quantum number.