That can tell you how large the file is. That usually, but not always, means how much it's been compressed.
Bitrate of uncompressed audio depends on the number of channels in the file, the sampling rate, and the bit depth. CD audio is stereo (2 channels) and has a bit depth of 16 and sampling rate of 44100 Hz. You just multiply all of that together to get the bitrate, which is 1411 kbps in this example. Some audio will have a sampling of 48000 Hz, or a bit depth of 24, or have just one channel. So you can't say for certain that a smaller file or one with a lower bitrate is more compressed, but most audio is CD quality. If you multiply everything out and the real bitrate is lower, it's compressed.
Then you run into the question of what kind of compression. Lossless compression makes the file smaller, but it will be bit for bit exactly the same data during playback. Think of it as a ZIP file, you can throw documents in and get them back out later without losing any words. Lossy compression has a still lower bitrate, but achieves this by discarding information we probably won't hear. Some codecs do a better job than others, and some formats are variable bitrate which are smaller than their equivalent constant bitrate brethren, and theoretically sound just as good.
There's other problems, too. Someone can take a low bitrate file, that's already been heavily compressed, and repackage it as a high bitrate file. This file will actually sound worse than the original, because the lossy codec discards additional information and pads it with meaningless data to get the desired bitrate. Lossy files can also be placed in lossless containers, which won't damage the file further but won't repair the damage already done. It'll technically be compressed, but not look like it.
The only surefire way to spot a compressed file is to open it in some sort of spectrum analyzer and look for a treble cutoff. Lossy files often cut frequencies off above a lower point because we probably won't hear it anyway.
Ultimately you shouldn't worry about it.