Shaders are short scripts that many games use to enhance their graphics, make light behave more realistically, objects change color, simulate refraction, add stylistic chocies (e.g. So in a nut-shell the answers to your questions are:

It also allows more realistic water surfaces and various effects such as lens flares, depth of view, blur effects, depending how the shaders are implemented.

Shaders allow for more realistic lighting modifications (imagine a colored lamp which colors the room, except where the player casts a shadow).

Now you could not only have high quality textures on blocks, but those blocks could react to lighting (for example they could be only half-lit), or they could cast shadows on each other.

What does that mean in context of Minecraft? Or any 3D graphics tutorial, because texture and shaders are some of the most fundamental things in 3D object rendering. If you want to find out about them more and have more technical details good start is Wikipedia:

In graphics it is used to simulate lighting effects, depth, other things. Shaders on the other hand, in 3D graphics, are a description language which defines how to change texture color, lightness and other things dynamically. Imagine that you have foldable tent in real life: the texture will be like the fabric that is put on the wire-frame. In context of graphics, each point is called a vertex, so a cube/block is made of 8 vertices and 6 faces. Take a wire-frame cube on which you put your own surface (texture). Textures define what an object's surface will look like:

Awesome shaders texture pack images