Some long time ago when I first heard the word 'inquisition', the context was the 'Spanish Inquisition'. These inquisitions took place in Spain during three hundred years beginning in the late 15th century. As a result, after inquisitions sometimes involving torture, thousands were found guilty of being heretics and were executed. But in England, an 'inquisition' was ordered for quite different reasons.
As we know, certain fortunate citizens in medieval England were granted lands and often knight's service to go with the premises. When such a landed individual died, the king's exchequer was informed. By writ, an order was issued to the escheator of the deceased's county of residence to hold an inquisition. The purpose was to enquire into what lands were held by the deceased, by what right he or she held them, whether a valid heir existed, and whether any such heir was 'of age' to legally inherit. The escheator also assessed the value of the lands inherited, according to which a 'fine' was collected by the Exchequer. In return for the fine, the king gave his confirmation of the heir's seisin (valid title to hold land).
A common order from the king might read: John held the manor of Watford of the king by service of a quarter knight's fee, worth 100 shillings per annum, and his next heir is his son Robert, aged 22 and more. If the same order recorded that Robert was aged 11, for example, then the lands were given into the hands of the king until Robert came of age. Frequently, Robert and his lands, in such a case, would be granted into the care of a ward who was compensated for his trouble. Or, in a problematic case, when the escheator found that for whatever reason John did not hold the manor by valid right, then the manor would be escheated back to the Crown.
There were other kinds of inquisitions. An inquisition ad quod damnum was a special inquisition held to enquire whether any damage would be done to the king by a proposed transfer of land from one person to another. Again, an inquisition could be convened by a writ de etate probanda. This was a special enquiry intended to assess 'proof of age'. In the foregoing case, such an inquisition would determine that Robert had indeed turned 21, to assure the king that Robert was now able to hold land.