Midpoints show the merging of two planetary energies. For example, the Sun/Moon midpoint shows how your identity and emotions come together, how you express your emotions through your personality, and also symbolizes close personal relationships.
The Mars/Venus midpoint can show our passions in relationships, or sex in a romantic way. The sign and aspects these points make shows how this merging is expressery ed. The easiest way to calculate midpoints is to convert the zodiac into 360° format (or look up a midpoint calculator.) For learning about calculating midpoints by hand, Cafe Astrology has a really informative article on this. (the site says the Sun/Moon midpoint, but it can be used for any midpoint.)
For this technique, I will be using the 360° zodiac format. For an example of the Sun/Moon midpoint interpretation, I will use my chart.
My Sun = 1°13' Cancer
My Moon = 7°49' Taurus
Sun/Moon = 4°30' Gemini
Any planets in hard aspect to this midpoint will be extremely important to a person's relationships and psyche. People usually ignore easy aspects when using midpoints and focus only on hard aspects (conjunction, square, opposition, quincunx)
The Sun/Mercury midpoint shows how we express our intelligence. How our intelligence fits into our personality.
The Mercury/Venus midpoint shows how we communicate in relationships, how pleasant our communication really is.
The use of midpoints not only applies to natal charts, but horary and relationship charts.