Nautical Terms
Running (before the wind) means sailing in roughly the direction of the wind, with the wind behind you (G in the diagram).
Sailing on a beam reach means sailing more or less at right angles to the direction of the wind, by angling the sail to the wind appropriately (D and E).
Sailing on a broad reach means sailing at an angle to the wind, somewhere between a beam reach and running before the wind (F and H).
Sailing close hauled means sailing at an angle to wind, somewhat upwind of a beam reach (A and C). Yes, this really is possible! It’s not possible to sail directly upwind (B). Exactly how close to directly upwind it’s possible to sail depends on the design of the boat – and the loading, and the skill of the crew.
Beating (upwind) means making progress upwind by sailing close hauled alternately to one side of the wind and then the other.
Tacking is the process of changing from having the wind on your port bow to having it on your starboard bow, or vice-versa.
The port side of a boat is the left side; the starboard side is the right side (both when looking forwards).
Long (or short) legs are the (relatively) straight stretches of sailing between tacks when beating upwind.
There’s more about this at Points of Sailing.