The MMEL and MEL list items that can be inop while still dispatching the aircraft, it also lists any required restrictions of that system being inop.
I think FAA Policy Letter 34, which is the preamble for all MMELs, gives some of the best information:
First they set the basis of an MEL, that every system/function of the aircraft must be operation to dispatch. This restriction can be superseded by the MEL:
The following is applicable for authorized certificate holders operating under Title 14 Code of Federal Regulations (14 CFR) Parts 121, 125, 129, 135: 14 CFR require that all equipment installed on an aircraft in compliance with the Airworthiness Standards and the Operating Rules must be operative. However, the Rules also permit the publication of a Minimum Equipment List (MEL) where compliance with certain equipment requirements is not necessary in the interests of safety under all operating conditions.
Then they tell you that MEL includes items that are allowed to be inoperative along with any limitations:
The FAA approved MMEL includes those items of equipment related to airworthiness and operating regulations and other items of equipment which the Administrator finds may be inoperative and yet maintain an acceptable level of safety by appropriate conditions and limitations
The individual operator's MEL, when approved and authorized, permits
operation of the aircraft with inoperative equipment. Equipment not required by the operation being conducted and equipment in excess of 14 CFR requirements are included in the MEL with appropriate conditions and limitations. The MEL must not deviate from the Aircraft Flight Manual Limitations, Emergency Procedures or with Airworthiness Directives. It is important to remember that all equipment related to the airworthiness and the operating regulations of the aircraft not listed on the MMEL must be
The image below is from the 767 MMEL, as you can see it lists items that can be inoperative and the limitation. Some items carry many restrictions, such as anti-skid or a pack, others carry none, such as reading lights. The MMELs are available on the FAA's website, so it can be an interesting read.
I do not know why the terminology is backwards, I assume it comes from a time aircraft were much less complex and an list of required items was realistic. But if it only listed items that were required for flight, you could end up with hundreds of systems inop, with no direct requirement to repair them. PL-34 addresses this a little bit:
The MEL is intended to permit operation with inoperative items of equipment for a period of time until repairs can be accomplished. It is important that repairs be accomplished at the earliest opportunity. In order to maintain an acceptable level of safety and reliability the MMEL establishes limitations on the duration of and conditions for operation with inoperative equipment.
Operators are responsible for exercising the necessary operational control to ensure that an acceptable level of safety is maintained. When operating with multiple inoperative items, the interrelationships between those items and the effect on aircraft operation and crew workload will be considered.
Basically the take away from this is that an operator can not issue every MEL in the book and dispatch the aircraft. For example, it may be okay to MEL one AC pack or one AC pack temp control valve, but it would not be okay to MEL one pack and the temp control valve on the other pack.