What is 5G New Radio (NR), and what techniques does it use to deliver its improvements?

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5G NR is the new air interface (radio access network) of 5G, designed to support fibre-like broadband (eMBB), large-scale M2M (mMTC), and ultra-low-latency links (URLLC). It uses a wide spectrum (kHz to mmWave), new OFDMA modulation/coding, aggressive frequency reuse, Massive MIMO, and a lean base-station design.

* OFDMA assigns orthogonal subcarriers to users. — Kanso & Maalouf, Public domain, via Wikimedia Commons. *
What NR is: a set of standards extending wireless communication — 5G essentially comprises the radio access network (the air interface, called 5G New Radio) plus a new core network architecture. NR's key aim is to grow wireless communication by efficiently using a larger frequency spectrum for mobile broadband.
The improvements NR brings:

Wide spectrum: from a few hundred kHz up to mmWave — enabling diverse use cases, cell sizes, and data rates
New modulation: OFDMA (Orthogonal Frequency-Division Multiple Access) and new channel-coding techniques
Frequency-reuse algorithms that work even in high-density environments
Massive MIMO (many antennas)
Low latency via lean design: a "functional split" in the base station designed for ultra-low-latency communication

The three design targets map to the use cases: NR was built (1) for fibre-bandwidth transmissions → eMBB, (2) for low-bandwidth large-scale M2M → mMTC, and (3) for extremely low-latency transmissions (vehicle-to-vehicle/infrastructure) → URLLC.
Tip: NR = the radio half of 5G. The other half is the cloud-native 5G core. Together they replace LTE's E-UTRAN + EPC.
Go deeper:

5G signals: OFDM waveforms, Frame Structure, and Numerology (MATLAB) — animated walk-through of how NR builds the OFDM waveform and why it offers multiple numerologies (subcarrier spacings) — the clearest single video on NR's waveform.
 Numerology / SCS (Subcarrier Spacing) in detail (ShareTechnote) — NR's flexible numerology (15/30/60/120/240 kHz via 2^µ·15 kHz), how symbol duration and cyclic prefix scale, and why mmWave needs wider spacing — far deeper than the generic OFDM articles.
 Orthogonal frequency-division multiplexing (Wikipedia) — the multi-carrier modulation OFDMA is built on; how closely-spaced orthogonal sub-carriers pack data without inter-carrier interference (and the carousel's diagram source).