Blackbody radiation is thermal radiation from a hot object emitted over a continuous range of wavelengths. But why are spectral lines, lines (i.e., you only get certain wavelengths when an element is heated up and you look at it's emission spectrum)? Is it because the light from the heated element is passed through some sort of diffraction grating?
This question is closely related to the question "If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons?".
While this technically isn't an exact duplicate of the link above, a similar conceptual explanation applies, namely that for complicated strongly-coupled quantum systems (like a hot chunk of metal), the energy spectrum is so complicated that for all intents and purposes it gets "smeared out" into a near-continuum, which (along with the fact that systems don't need to be completely on-resonance with external EM light to be able to absorb or emit) means gives an intuitive flavor of why continuous spectra happen.
Meanwhile, for relatively simple things like gas-phase atoms, the energy spectrum is simple/sparse enough that you can actually resolve individual spectral lines (unless the coupling to the surroundings becomes non-negligible, such as in the case of pressure broadening, which is partly responsible for the comparatively broad-spectrum appearance of high-pressure sodium vapor arc lighting used on streets and major highways).
So in essence:
Simple things (like individual atoms) have simple, sparse spectra; complicated things (like chunks of hot metal) have complicated, near-continuous spectra.
Also, you'd be surprised at how quickly the spectra of quantum systems devolve into an absolute chaotic mayhem: in acetylene, which is a 4-atom molecule, there are entire binders hundreds of pages long which contain tens of thousands of spectral lines, which for all intents and purposes means that the molecule has a near-continuous rovibronic spectra. For systems with 5 atoms or more, it's completely insane, and for a chunk of metal (with trillions of atoms or more) it's not hard to see why you might expect to see a continuum component to its emission spectrum.