How come the photosphere shows absorption lines and the chromosphere and corona show emission lines?

Short-form answer: because the photosphere is cooler than its background (the upper part of the solar interior where the contiinuum light arises), whereas the temperature is rising through the chromosphere and corona. Going all the way back to the set of Kirchhoff's laws for spectroscopy (not Kirchhoff's laws for circuits or thermodynamics...), that's when you see emission lines.

Slightly longer answer will depend on the spectral features. The contrast of the chromosphere, in particular, is much greater in emission lines that coincide with photospheric absorption features (hydrogen Balmer lines, Ca+ H and K lines in the violet. The temperature contrast make sthe most difference in the UV, where one sees mostly the upper layers of the solar atmoephere, and even more pronounced for X-rays, where the photosphere is just black.

Sorry I still don't think I understand. My book says about Kirchoff's laws,

Emission Lines: "A low density hot gas emits light whose spectrum consists of a series of bright emission lines."

Absorption Lines: "A cool thin gas absorbs certain wavelengths from a continuous spectrum, leaving dark absorption lines in their place supermimposed on the continuous spectrum."

But why the difference in the photosphere and corona?

Because the corona is so much hotter than what lies below (the reason being a whole different thread...), while the photosphere is not.

Think about "hot" and "cool". With respect to what? Photospheric gas, if you saw a box of it glowing by itself, would be a source of emission lines. However, in front of the solar interior, which is much hotter, it gives off many fewer photons in an emission-line wavelength than it absorbs from the background, so the net effect is still an absorption line. Similarly, the very hot component of the interstellar medium that forms O(5+) is occasionally seen as a source of emission lines near 1030 A in the far-UV, but it's much easier to see in absorption when there is a bright background source. (Just to complicate things, "hotter" and "cooler" need not refer to thermodynamic temperature, but more nearly to brightness temperature - the temperature of the blackbody which gives the same surface brightness at the relevant wavelength. Nonthermal processes can work just as well, as in the continuum light of the Crab Nebula).

Indeed and Nebula can show strong Emission

http://praxis.pha.jhu.edu/pictures/pneb_spec.gif

this site explains things on spectra a little bit
http://astrwww.astr.cwru.edu/reference/spectra.html

It is merely a question of brightness contrast. If you observe a light source against an even brighter background it will appear relatively darker (i.e. in 'absorption').
So if the continuum background of the lower solar atmosphere is brighter than the emission lines of the upper layers, the latter appear to be in 'absorption'. The continuum of the solar corona is very weak, so the coronal lines appear to be in emission relative to this, but against the bright continuum of the solar disk they would appear in absorption. On the other hand, if you could view the gas that produces the light in the absorption lines against the dark sky instead of the bright continuum of the photosphere, you would see them as emission lines.
It also depends on the wavelength region you are considering: the solar Balmer series lines in the visible region for instance appear in absorption, but the Lyman series lines in the ultraviolet appear in emission, not primarily because they are stronger, but because the continuum in the ultraviolet is much weaker.

By the way, the expression 'absorption' lines is somewhat misleading: there is actually no light being absorbed in the corresponding gas volumes but it is merely being scattered back into the lower layers. Spectral lines therefore merely tend to block the radiation that is emitted from the lower layers. True absorption would be due to photoionization and this would affect lines and continuum to the same degree and hence not change their relative intensity.

No, it is not a matter of contrast. Light that passes through a (relatively) cool gas on its way to the observer from a hot object is dimmer than it would be without that cool gas in the way. Energy is actually absorbed from the light beam.

A not-too-inaccurate way of thinking of it is that a beam of light has a temperature associated with it (same as the temperature of the body that produced it, assuming that body is big/opaque enough). The longer that beam spends passing through a gas, the closer its temperature becomes to that gas. And, of course, hotter light is brighter.

Lol, what's right and what's wrong???