Theoretical condensed matter here (though not an expert on strange metals specifically). The idea is that in a quantum many-body system, a (low-energy) state can often be represented as a set of independent excitations of the field, which are called quasiparticles. The "particle" picture for the Fermi liquid already operates in a framework of quantum fields. "No quasiparticles" means that there is no such representation, i.e., you can't say something like "these two states differ by an addition of a particle with such-and-such properties."