A photon can have one of an infinity of polarizations. These states are describable as a mixture of any two orthogonal polarizations (a "basis"), such as "horizontal" and "vertical". "Left circular" and "right circular" are another choice.
The funny thing happens when you measure "how much" a photon is polarized into any given orientation. It appears as being polarized either in that orientation, or in the polarization complementary to what you measured. E.g., horizontal or vertical. The outcome is determined with a probability based on the actual polarization of the photon prior to your measurement. Then – the funny thing – the photon takes on that polarization. Repeated measurement using the same basis gives the same results. Measure again with a different basis, and the game starts over again.
You can see this in the macro world with a laptop screen and two pairs of polarizing sunglasses. Using one pair of sunglasses, you should be able to block the light from the screen entirely – you are holding them perpendicular to the polarization of the screen. Place the second pair in between the first and the screen, and rotate it. At certain orientations, you will be able to see the screen! The second pair (nearest the screen) is diagonally polarized, and will "convert" the light from the screen into that polarization, before it reaches the first pair (furthest from the screen), which is orthogonal to the screen only.
(Note: Things change completely once a second photon enters the picture. It can be entangled with the first, and their states are no longer independently describable. Measurement of one affects the pair.)