A Berg connector - later known as a DuPont connector, or IDC connector ('insulation-displacement contact') - is a very common family of computer connectors.
They use pins in parallel rows, with .1 inch pitch (both betweeen rows for multi-row connectors, and also between the pins in a row).
The originals used 'male' and 'female' plasic shells and pins: male pins in female shells (which went on printed circuit boards using through-holes); and female pins in male shells, which went onto the ends of cables, with individual female pins crimped onto the wires of the cable.
In fairly short order, the physically compatible IDC connector for use with flat cable was developed; it has short teeth which cut through the insulation around the wires in the flat cable (hence the name), and simply crimps onto the flat cable, thereby making cable production much faster, easier, and more reliable.
The connectors which go onto boards are now often called 'headers', and they are available in 'straight' (the pins point up) and 'right-angle' (the pins point sideways) form; the crimp-on connectors are now available in male and female forms.
Original Berg connectors were 40 pin, with the pins 'numbered' from the DEC alphabet, from 'A' to 'Z' (an extension of the classical, which stopped at 'V'), and then 'AA' to 'VV'. Facing the pins in the header, with the PCB at the bottom, pin A is on the left, at the bottom, with 'B' above it, etc.
IDC connectors come in a large variety of sizes (from 1 pin to 64, and perhaps larger), with one, two or three rows of pins. The pins are now identified by numbers; with the header in the orientation as above, pin '1' is in the upper right corner, with pin '2' immediately below it.