The Wandering Days are what the Hobbits refer to as the period of time that they had begun their great migration from the upper Vales of Anduin and the feet of the Misty Mountains, and into various parts of Eriador and finally to what would be known as the Shire.
For some millennia, the hobbits lived relatively peaceful and comfortable lives in the upper Vales of Anduin and at the feet of the Misty Mountains, but by the mid-twelve century of the Third Age things started to change and life was becoming difficult for them. Men were beginning to increase in the lands near them and with Sauron occupying Dol Guldur, the long and peaceful forest of Greenwood the Great was becoming evil. Beginning in TA 1050, the migration began but not all at once as only the Harfoot tribe was willing to made the journey over the Misty Mountains. The Fallohides and the Stoors joined them in TA 1150.
The Hobbit tribes settled in many different places in Eriador. The Harfoots went over the mountains making it as far as Weathertop and were later intermingled with the Fallohides settling there in the Weather Hills for a time. The Stoors, who climbed the Redhorn Pass through the mountains, settled in the Angle and Dunland, living there for many centuries. In the Angle, they were intermingled with both the Fallohides and the Harfoots in a series of settlements known as the Forgotten Villages.
With the threat from Angmar worsening, the Stoors in the north moved south to Dunland with their kin, some even returned to the Vales of Anduin, settling in the Gladden Fields, and were probably the ancestors of Déagol and Sméagol. By TA 1300 mixed groups of hobbits began settling in Bree-land, especially in the village of Staddle where they lived peacefully side by side with the Men of Bree. Breeland was their home for over three-hundred years until TA 1601, when King Argeleb II of Arthedain granted them the land between the Far Downs and the Brandywine river. Large mixed groups of hobbits migrated there during that year and later, in TA 1630, the remainder of the Stoors of Dunland moved there as well. Some hobbits chose to remain in Bree, where they lived ever after.
These events are considered ancient history and are recorded in the first known written records that mention Hobbits. Their oral tradition goes back no further, so that their ultimate origins are unknown.