Neither the show or the books really get into Jeor Mormont's reasonings for being at the Night's Watch. As one of the older generation, in the book's history instead of the present day events that the series covers, and as mostly a bit character, Jeor is not given much attention. As other's have mention, Jeor abdicated his seat as Lord of Bear Island and head of House Mormont. He voluntarily goes to the Wall, so his son took over.
It's really so his family and land can prosper. Given a bit of background, we can guess why.
First, Bear Island and House Mormont, while noted as a reputable house, a bannerman of Winterfell, it was not particularly prosperous. Small, poor, not much land, a modest castle.
Second, Jeor is old. Jorah is not.
Third, he gives up his place roughly right before, or during the rebellion against the old Mad King by Robert Baratheon.
Fourth, aside from Jorah, there is no male to take over.
Fifth, if someone is requested to become Kingsguard, they take a vow against owning land or marrying.
Combining these facts, you can make an assumption that Jeor did it to ensure that House Mormont is well taken care of, and the Bear Islands are kept in the House Mormont's name. Also, that had he not joined the Night's Watch, it would have had to be him, as Ned Stark's bannerman, to fight in the rebellion. With Jorah as head of the house, he would be the bannerman, and he could not be obligated to join the Kingsguard, a possible outcome. He would also be a better fighter than Jeor, and any accolades Jorah would receive would be good for House Mormont. It was a calculated move, by a wise man, who knows the politics of Westeros well. Remember, Westeros culture heavily favors family over individuals, and the land over the family.
Of course, Jorah goes and ruins it by selling slaves against the law, because his wife likes fancy things, but hey, kids, what can you do, right?