ε-NFA
Also known as: λ-NFA, epsilon-NFA, lambda-NFA
An ε-NFA (Linz: λ-NFA) is an NFA that may also move on the empty string: edges labeled $\varepsilon$ / $\lambda$ that read no input.
Those free jumps are glue. Thompson construction invents them so every regex operator wires the same way (one entrance, one exit). They are not a deeper feature of regular languages; you delete them later.
To run or to convert: take ε-closure after every real symbol (and at the start). Collapse ε-paths into ordinary letter edges to get an NFA, then optionally subset-construct a DFA.