FH,
Normally for Cat A in Europe (broadly CAA/JAA) the broad outline is that in the event of the failure of a critical power unit (usually one engine failure, but they write the rules to cover helicopters with more than 2 engines) the aircraft must be able to either safely land back on to a suitable surface or continue the flight to a place where a safe landing may be made. For helicopters where the CDP is at greater than zero knots, the helicopter must be rejected back on to a sujitgable prepared surface before it reaches CDP. At CDP the pilot has the option of continuing or rejecting and after CDP he will normally continue to climb away on one engine. (I say he has the option, because in the event of an engine failure after CDP on a large airfield it may be preferable to reject the take off). The aircraft must then be capable of climbing to set criteria, depending on altitude, temperature and weight, at Vtoss to 200 feet and there it normally accelerates to Vy and has to be capable of maintaining a rate of climb at Vy of 150 feet per minute on 30 minute/MCP to either 1000 feet above the take off elevation, or to MSA if IMC. At 1000 feet above the surface (or MSA if IMC), it must be capable of climbing at 50 feet per minute on one engine at Vy at 30 minute power/MCP (some helicopter performance charts cover only one or the other of these power ratings). When approaching to land, in the event of the failure of a critical power unit it is committed to land after the LDP. When carrying out its landing it must be able to do so safely, so a twin engine helicopter, with a wheeled undercarriage, rejecting on to a waterlogged grass surface and rolling over as one wheel digs in, is not operating to Category A.
Category B is a relaxation of the Cat A rules and says that at times there may be a period during which the helicopter may be at risk during the take off procedure. During this period the aircraft may not be able to land safely, but if it does have to land it must be able to do so without damage to its occupants or third parties outside. When it reaches a 'Defined Point' it must then have Category A performance. The defined point varies in different countries and organisations. In many countries this will be when the helicopter attains Vy.
The rules vary a bit in different countries and are more detailed than this, but that's a basic outline. I'm sure there will be many other contributors to this forum far better qualified and more knowledgeable than myself who can considerably expand on what I've said and who will correct any errors I have made.....but I hope this helps a bit
Soggy