Chaining is simply the act of encountering the same Pokémon over and over again, which will give you better shiny chances and help you get special features on the Pokémon.
For example, you could get HA Pokémon, higher level Pokémon, Pokémon not native to Hoenn, Pokémon with better IVs or Pokémon holding a special item.
You can also chain in some other games, like XY with the Pokéradar.
>To use the Poké Radar, you first have to charge it up by walking 50 steps. Then you have to be standing in grass or flowers where wild pokémon can appear. When you use the radar, some patches of grass around you will shake. Those shaking patches have wild pokémon. Step into the shaking patch to encounter a wild pokémon.
>After you use the Poké Radar and defeat or capture a pokémon that you found in a shaking patch of grass or a bubbling spot on the water, the background music will be different, and grass around you will shake again. If you find the same type of pokémon in the next spot, the grass will shake again after you defeat or capture it. When you keep finding the same pokémon each time, it's called chaining. During a chain, the background music will continue to be different from the usual background music.
>The longer you chain, the more likely you are to encounter a shiny pokémon. The shiny probability reaches maximum after you have chained 40 times. If a shiny is in a patch of grass, the shiny patch will sparkle and make a different sound. In addition, the background music will be different if a shiny patch is available.
Pokérader is usually harder to use, however
>Similarly to the Poké Radar, hidden Pokémon can also be chained, though chaining with hidden Pokémon is easier than with the Poké Radar.
>A chain builds every time the player captures or defeats a hidden Pokémon of any species. If the player does not capture or defeat the Pokémon (whether the player chooses or is forced to flee, such as by Roar, or the Pokémon escapes, such as by Teleport), the chain breaks. A chain will also break if, outside of battle, a hidden Pokémon appeared and is not encountered (whether by scaring it away, waiting too long, walking too far away, leaving the area, or entering a different battle). The chained Pokémon do not need to be found using the Search function, and the message "The Pokémon couldn't be found. Try looking in a different area!" does not break the chain if received when the Search function is used.
>The level that hidden Pokémon appear at increases by one for each five successive encounters. Every 100 encounters, this level bonus resets to zero.