Lures enable you to catch specific fish.
Each fishery and each fish have their own lures, excluding the Boss fish. Generic fishery lures will let you catch any fish available at the fishery.
Once chosen, a specific fish lure will increase your chances of catching that fish by the percentage given in the lure description. More details on catching not only the desired fish but also bigger ones you can find here.
Each lure can be upgraded to a higher level after obtaining the required number of lure points. Upgrading lures will grant you experience points. Gaining enough experience points will let you go up a level. Every few levels, you will be able to open a new fishery.
Packs or lures can be obtained from the in-game shop. Every 24 hours, you'll have a chance to purchase up to 3 randomly-picked lures from the shop.