How did the universe evolve?

If the Universe is expanding, it means that once it was much smaller than it is now. Arno Panzias and Robert W. Wilson made an important discovery in 1964, while working for Bell Laboratories. They were trying to understand the source of background signals which interfered with radio communications. (Arno Panzias is currently director of ATT Laboratories; Panzias and Wilson shared the Nobel Prize in Physics for the work mentioned below). During their work, they found that there was a constant background signal with a wavelength of 7.35 cm. The intensity of this signal was uniform over the entire sky. They measured the "temperature" of this radiation which is supposed to come from the beginning of the expansion of the universe. This electromagnetic radiation (cosmic background radiation) has a spectrum (or pattern of intensity as a function of wavelength) characteristic of a "black-body" at the temperature of 2.73 K (degree Kelvin, i.e. 2.37 degrees from absolute zero; melting of ice is at 273 degrees in this scale) or, equivalently, has a characteristic wavelength of 7.3 cm ( black-body radiation is the electromagnetic radiation that is emitted by a body of matter.
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Such measurement is consistent with the theory of an expanding universe, since, as the universe expanded, it cooled.
If we take the currently observed expansion and we extrapolate back into the past (assuming a roughly constant rate of expansion), we find that the universe was point like object 8 to 15 billion years ago (the wide range of age depends on the uncertainty in the determination of the Hubble constant, an active research area even today). At the beginning the universe was extremely hot and dense (more about this later) and as it expanded it cooled. The radiation that Panzias and Wilson measured is the remnant signature of this expansion. In other words, in the initial stages the universe cooled rapidly and reached a temperature of about 3 K. At that temperature, a body emits radiation which has a peak in intensity at about 7.35 cm.

An objection can be raised. If the measured temperature of the universe
is 3 K, how do we explain the fact that there are planets, such as ours, and stars where the temperature is much higher?
The reason is that electromagnetic radiation interacted with matter only in the very first minutes of the universe. Afterwards it became "de-coupled" and electromagnetic radiation and matter didn't interact any longer.
Note: this electromagnetic radiation of a black-body at 2.73 K is the remnant of a radiation present at the beginning of the universe. Obviously, radiation is created all the time, as in stars, but this latter one doesn't concern us at the present time.

Another way to think about it is that at the beginning the universe was extremely dense and hot. As it expanded and cooled, it ceased to be in thermal equilibrium; now there are lumps of matter (stars, galaxies) which are much hotter; however, the signature radiation of the expansion still permeates the universe.

COBE map of the cosmic background radiation; variations with
respect to the average are indicated in colors (red:hotter, blue: cooler).

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Internally related links:
spectra of stars