Muting strings can have different effects depending on what you are trying to do. The act of muting is simply using you palm of you pick hand, (palm mute), fingers of your pick or fret hand, or any combination of those, to muffle the sound of the string or strings that need to be muted. There are various stages of muting to barely at all to extreme muffled. Good muting technique is used in every path of music but very much in the metal arena where a good palm mute gives the rhythm section a deep hard core heavy sound. Listen to any MetallicA cd to see what i mean.
Take a look at Ex.1, this is a heavy rhythm line relying on palm mutes on the open E string. Try this with attitude and a good strong mute in distortion to see what i mean, also work it up to a good fast tempo.
Now take a look at Ex.2 and notice that this time there are x's on the string instead of the pm above it. Either way means to mute the desired strings. Try this neat little rhythm section out and see how you like it.
One other quick thing to look at is chords, depending on thier structure will have muted strings in the middle of them. You have to use the edge of your finger to mute the string, (up to you which one), so the chord can still be strummed without the muted string sounding. Try the Am6 chord below in Ex.3 to see for yourself.
Now take a look at Ex.4 and notice that you can mute an entire riff if you like. I would use a medium type mute here so you can hear each note clearly but they still will sound deep and heavy.
That's about all there is to muting strings. Try to use this technique in your soloing and rhythm and you can thank me later because i know you will like it. This technique is similar to bends in that it is easy to learn but hard to master so start practicing now.