We all have been seven years old, we all have known seven-year-olds. First or second grade, full of enthusiasm, at that awkward age where you know what you want but the grownups are still enough bigger that if they don't want it too, it's not going to happen. Still young enough to be characterized as "tiny tots."
A medieval seven-year-old was considered old enough to know right from wrong, to have reached some version of "the age of reason." (Various stages kicked in at seven, fourteen, and twenty-one. The only one we still keep is twenty-one, though some states used to allow driver's licenses at fourteen.) For example, they could give consent to a donation.
Although birthdays and exact ages were far less important to medieval people than they are in modern times, momentous changes could happen to a child around age seven. This was the stage when their future life might be decided.
It was at roughly this age that a boy (or more rarely a girl) would be sent off to a monastery as an oblate (literally an "offering"), if the parents decided this child was going to become a monk (or nun). Contrary to popular belief, parents were not disposing of excess children. Many large families sent no one to the monastery; others ended up having the entire family enter the cloister. And of course a large gift was expected to accompany the child, so it was certainly not a way to "get out of" the expense of child rearing.
Going into the monastery was a one-way trip. An oblate would rarely if ever see his family again, unless he decided not to become a monk after all. This decision would be made around age fourteen. In practice, few boys or girls brought up in the cloister, not knowing anything else for seven years, decided to leave.
Alternately, parents might send a boy (not a girl) off to the cathedral school, to start training to become a priest. Here at least the child would get to see his family again, and if the family lived in town, the boy might be a day pupil, coming home every night (or at least every few weeks). Here the basic reading and writing a boy had learned from his mother would quickly be augmented with rigorous Latin and theological training. Even those who did not intend to become priests might go to a cathedral school as a day pupil; the future King Louis VI of France was one example.
Parents who wanted to apprentice their children to a trade would send them off around age seven as well. Although they would still see the child intermittently, the child would live with the master with whom he (or sometimes she) was training. And again, a large donation was expected to set a child on this path. (See more here on guilds and apprenticeship.)
If a family was aristocratic, in the twelfth century or later, the age of seven or so was the age at which boys would be sent off for knighthood training, either with a lord or with an uncle or other appropriate relative. Again, the child might come back to visit, but his home now was where he was being trained. (See more here on knighthood training.)
Girls were less likely to leave home at age seven, because they weren't trained as knights, were less likely to apprentice in a guild (most guilds, even though not all, were male-dominated), and did not become priests. The majority of nuns were adult converts, not child oblates. But by age fourteen a girl, who had been taught both book learning and household management skills by her mother, would be considered old enough to marry.
Of course, the seven-year-old child of a peasant family had fewer possible options; he or she would be expected to start actively helping out in all the chores associated with farming--and to know enough not to be stepped on by the ox.
(See more here on medieval childhood.)