Why MONERO (XMR)? Privacy-Centered digital currency

Monero launched on April 2014 as a fork of Bytecoin. Bytecoin was an obscure cryptocurrency that, while having pioneered a novel way to achieve privacy, was plagued with a shady history and an unfair launch. As a result, the community forked the code of Bytecoin and began a long, multi-year project of cleaning it up, documenting it, and getting the fundamental aspects of it right.
Monero focuses on providing strong privacy by default while offering optional transparency, allowing its users to selectively disclose their transactional history to selected parties. Privacy is inherent to the protocol and requires no additional steps (interactivity) from the user. As a result, fungibility is greatly improved as well.
Monero's architecture provides a clear separation of the node functionality and the wallet. Originally having just a command line wallet, which was deemed too difficult for non-technical users to use. The second beta of Monero’s Graphical User Interface (GUI) was released in late March 2017.
Apart from its novel privacy features, Monero offers several improvements as compared to Bitcoin, both in its core cryptography (like using the ECDSA Curve25519 made by renowned cryptographer Daniel J. Bernstein and Schnorr signatures) as well as its interesting economic aspects, such as having a dynamic block size and fee system, and a constant tail emission of coins corresponding to a yearly inflation rate of around 1%.

About Monero Privacy
In Bitcoin, transactions are traceable as the transaction graph is visible in the blockchain; sender and recipient addresses as well as transaction amounts are visible. This makes Bitcoin vulnerable to coin tainting and susceptible to blockchain analysis, thus potentially significantly reducing its fungibility and usefulness as digital cash (which should be indiscernible from any other coin). Various techniques have been proposed and utilized to improve Bitcoin's privacy, however they either suffer from having to trust centralized services (coin mixers) of dubious quality and legal status, or from requiring manual user intervention and coordination (such as CoinJoin).
Providing privacy and fungibility by default is considered a core tenet of the Monero project. Monero obscures the transaction graph and hides transaction amounts by a combination of Ring Signatures and Confidential Transactions, and hides user addresses via the use of Stealth Addresses.
Monero is closely related to the Kovri project, which implements an I2P client in C++. Once it is production-ready and integrated into Monero, Kovri will also help obfuscate user and node IP addresses, making it less susceptible to network metadata analysis.

We shouldn't be making the mistake of saying that we don't need increased privacy because we have nothing to hide. This is a slippery slope to saying we don't need free speech because we may have nothing to say, or the equivalent of permanently removing the shutters/blinds from our house.
Fungibility and privacy are important enough topics for Bitcoin as well, since they took the central stage at the recent Scaling Bitcoin conference in Milan. It's a tricky problem and one that involves complicated cryptographic schemes that are understood by few (so far), and are not very accessible to the average user, without a practical way to hide the complexity.

Monero Fungibility
Fungibility is a good or asset's interchangeability with other individual goods or assets of the same type.

So while it is inaccurate to say that “A dollar is a dollar,” it is indeed accurate to say that “A Monero is a Monero.” through complete privacy it achieves homogeneity, and through homogeneity it achieves fungibility.

References:
-The Monero Project
-Emile Phaneuf, Why Monero might be the most fungible currency in history
-University of Nicosia Blockchain Initiative, Introduction to Digital Currencies