Thomas' answer is completely correct, I'd just like to elaborate a little on the reason for such a spectrum.
Quasar spectra generally have broad emission lines, in particular Lyman $\alpha$ at a rest wavelength of $1216\,\mathrm{Å}$, originating from hydrogen being ionized by the quasar's strong UV continuum. The hydrogen quickly recombines, and roughly ~2/3 of each recombination results in the emission of a Ly$\alpha$ photon.
Nearby quasars
A typical spectrum of a nearby quasar (3C 273; the first ever to be identified) is seen here:
Credit: Jannuzi (1996).
3C 273 lies at a distance of 2.2 billion lightyears and consequently has a redshift of $z=0.158$, so we observe the Ly$\alpha$ emission line at $\lambda_\mathrm{obs} = (1+z)\lambda_\mathrm{em} = 1408\,\mathrm{Å}$. A broad absorption line is seen at $\lambda=1216\,\mathrm{Å}$; this features is not from the quasar, but is imposed on the spectrum by neutral hydrogen inside our Milky Way, as the light completes its final part of its journey.
Moderately distant quasars
The next figure shows the spectrum of the more distant quasar PG 1634+706:
Credit: Jannuzi (1996).
The spectrum looks like the one above, except that 1) the Ly$\alpha$ line is redshifted to $2837\,\mathrm{Å}$ (because the quasar lies at $z=1.334$), and 2) the part of the spectrum blueward (left) of the Ly$\alpha$ lines display a bunch of little absorption lines.
Before investigating this, let's take a look at an even most distant quasar, Q1422+2309 at $z=3.63$:
Credit: Jannuzi (1996).
Again, we see the Ly$\alpha$ emission, but now the blue part of the spectrum shows even more, narrow absorption line.
The Lyman $\alpha$ forest
What going on here? This is the so-called Lyman $\alpha$ forest: As the spectrum of the quasar leaves the host galaxy and begins its journey toward Earth, it is slowly redshifted. After a while, the light meets a diffuse cloud of neutral hydrogen, causing an absorption line$^\dagger$, just like the Milky Way did in the case of 3C 273 above, except that this cloud is not a full-blown galaxy like the Milky Way, but a much small, intergalactic cloud of gas.
When the light meets this cloud, it has already been redshifted a little bit. Hence, although the absorption takes place at a rest wavelength of $1216\,\mathrm{Å}$, the absorbed light started out with a slightly bluer wavelength of, say, $121\mathbf{5}\,\mathrm{Å}$. Shortly after, the light meets a new cloud, causing absorption at a wavelength that started out even bluer.
The result is that all the light that started out bluer than the emitted Ly$\alpha$, and that happens to meet a hydrogen cloud at a point in space where it has been redshifted to $1216\,\mathrm{Å}$, experiences an absorption line.
This feature — the wealth of narrow absorption lines blueward of a Ly$\alpha$ emission line — is called the Lyman $\alpha$ forest (LAF) due to its resemblance of… um… trees… -ish…
Evolution of the intergalactic medium
So why does 3C 237 show almost no LAF, PG 1634+706 shows a little, and Q1422+2309 is full of "trees"?
The reason is that 1) the Universe was more neutral in the past so there were more clouds to absorb the light, and 2) the Universe was smaller so there clouds were closer together.
What then happens if we observere even more distant quasars?
The Gunn-Peterson trough
As we approach $z\sim6$, what we see is that the LAF lines eventually begin to become so numerous and overlap, that in the end all light is absorbed, as seen in this spectrum of J2315–0023:
Credit: Becker et al. (2015).
Predicted by Gunn & Peterson (1965), and hence named the Gunn-Peterson trough, this effect was only observed much later (Becker et al. (2001).
In other words, the answer to your question is "The interpretation of the DESI spectrum is that it is emitted by a quasar so distant that we see it at a time when the Universe was much more dense and neutral than it is today".
The Epoch of Reionization
So, if the Universe was so neutral in the past, why is it so ionized today? What happened?
The culprit is the first stars and galaxies, emitting an abundance of hard, ionizing radiation that started to fry the Universe (and to a lesser extent, quasars, although we now believe that their impact was sub-dominant). This process lifted the Universe out of its Dark Ages and re-ionized it ("re-", because it had been ionized before, until it recombined 380.000 years after the Big Bang).
Although reionization is caused by the first luminous sources, appearing 100–200 million years after the Big Bang at $z\sim20\text{–}30$, it took a while to "penetrate" the intergalactic medium. The exact course of the process is a hot topic, but in the current paradigm reionization is believed to begin as "bubbles" of ionized hydrogen around galaxies that eventually overlapped and rendered the Universe largely ionized by $z\sim6$.
The last figure shows a bunch of observations and models of how the global neutral fraction of hydrogen decreased from $x\mathrm{HI}\sim1$ (i.e. mostly neutral) at $z\simeq12$ when the Universe was ~400 million years old, to $x_\mathrm{HI}\sim0$ (i.e. mostly ionized) at $z\simeq6$ when the Universe was ~900 million years old.
Credit: Naidu et al. (2020).
As discussed in this answer, however, residual neutral hydrogen was enough to cause much absorption for several billion years after the Epoch of Reionization.
$^\dagger$In fact it is not really absorption, but scattering. The photon which has been redshifted to $1216\,\mathrm{Å}$ excites a neutral hydrogen atom, which de-excites after some $\sim10^{-9}\,\mathrm{s}$, emitting another Lyα photon in another direction. But since the photon hence is removed from our line of sight, in effect this is the same as absorption.
