Sight-reading (or sight-singing for singers) is the ability to play music that one has never seen before. It is important to be able to read music well in order to sight-read.
People who find it hard to read music will find it hard to sight-read. The best way to improve is by regular practice. People who play in orchestras will need to be good sight-readers because they often have to play music that they have never seen or heard before.
People who learn the piano often find sight-reading hard because they have to read two staves at once (one for each hand). Playing through lots of easy music is a good way to improve. Playing piano duets with a friend is also great fun.
When someone is reading aloud their eyes are looking several words ahead of the word they are speaking. In the same way a good sight-reader will try to look ahead of the notes he is playing. The player is "anticipating" (thinking about what is going to happen next). In this way he can try to make the music expressive, even if it means leaving out some of the notes.
A good sight-reader will be able to see the printed music and imagine what the notes should sound like. In this way he will not need to keep looking at his fingers to check whether he is playing the correct notes.
Some pianists are very good at sight-reading. The pianist John Ogdon was able to read extremely difficult modern music at first sight.