A digital currency in which encryption techniques are used to regulate the generation of units of currency and verify the transfer of funds, usually operating independently of a central bank.
Cryptocurrency is the generic term for a large set of digital assets that use encryption techniques to generate units of currency, verify the transactions, and transfer value. Generally, cryptocurrencies are considered to be decentralized. Cryptocurrency should not be confused with virtual currency which is a type of digital money that is usually controlled by its creators or developers. Some examples of virtual currency are gametime in World of Warcraft, ROBUX in Roblox, reward points programs, or Ripple, all of which can be exchanged for currency or cash value, but are not considered cryptocurrency because they are centalized and controlled/issued by a single entity.
Monero is one of many cryptocurrencies currently available. Other examples are Bitcoin, Litecoin, Dogecoin, Dash, Zcash, etc, but nearly all other cryptocurrencies lack features that make them a true money (most importantly fungibility which is a requirement for it to be a store-of-value).
Not all cryptocurrencies operate the same, but they usually share the properties of decentralization, encryption, and the ability to send and receive transactions. Most are irreversible, pseudonymous, global, and permissionless. Most aim to be a store-of-value or be digital cash that allows you to transact.
Most cryptocurrencies (including Monero) use a distributed ledger (called a blockchain) to keep track of previous transactions. The blockchain serves to tell other users on the network that transactions have happened. There are many different ways for cryptocurrencies to create their blockchain, and not all are the same. Monero uses proof-of-work to craft blocks, where other cryptocurrencies may use proof-of-stake or other consolidated methods.
Ultimately, cryptocurrency is an attempt to create trustless value; that is free from borders, governments, and banks. Whether that be to transact or to be digital gold is up to the users of each.