A virtual particle is an internal contribution to a perturbative scattering amplitude, commonly represented by an internal line of a Feynman diagram. The line contributes a propagator, and its internal four-momentum is summed or integrated as required by the diagram. It need not satisfy the on-shell relativistic energy-momentum relation of an external detected particle.
For example, a virtual photon connects charged currents in electron scattering. This is a calculational contribution to the full interaction amplitude, rather than a directly observed photon flying between the electrons. Energy conservation and momentum conservation still hold at the vertices; off-shell propagation does not mean energy has been borrowed in violation of conservation. Individual virtual contributions can depend on the gauge or perturbative organization, whereas an observable prediction requires the appropriate complete amplitude.
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Virtual particles are a concept in quantum field theory that represent transient fluctuations in energy that occur in a vacuum. They are not "particles" in the traditional sense; instead, they are temporary manifestations of energy that arise during interactions between particles.