Machi
Machi is the Japanese term for "tenpai wait patterns". Given any mahjong hand at any instance, players are waiting for specific tiles either to develop their hands or complete it. Wait patterns arise during hand development, when mahjong tiles in possession in the hand are in need of other tiles in order to complete mentsu (melds) or the entire hand. Wait patterns during tenpai are of particular interest, simply because that is one of the main goals of hand development.
Mentsu
Mentsu are the tile melds used to develop and compose the hand. To form a complete hand, players must possess 4 melds and a pair. Though, there are three exceptions to the pattern, namely: chii toitsu, kokushi musou, and nagashi mangan.
Hand development
Tenpai wait patterns overview
Many patterns arise during tenpai, such that they are named. These patterns may develop well before tenpai, but they are of particular interest during tenpai. After all, it is in the best interest of the player to know wait tiles during tenpai, in order to not miss it or even choose to change wait patterns, if needed.
Basic wait patterns
Ryanmen
Waiting for: 
Penchan
Waiting for: 
Shanpon
- Waiting for:
Kanchan
Waiting for: 
Tanki
Waiting for:
Nobetan
Waiting for:
Mixed combinations
Ryanmenten
Waiting for: 
Sanmentan
Waiting for:
Chuuren poutou kyuumen machi
Waiting for: Any of the same suit tiles, 1 through 9.
Junsei Kokushi musou 13 machi
Waiting for: Any of the 13 tiles shown here.
Complex patterns
These combinations involve patterns that do not have specific names. Instead, they use combined forms of the other patterns. Furthermore, they mostly consist of consecutive, or closely consecutive, numbered tiles. Recognition of these patterns can produce some significantly powerful waits, which may be immune to suji and have large numbers of waiting tiles.
External links
ReachMahjong wait guide
Tenhou wait calculator
Japanesse Wiki Tenpai