Clipping and Caulking are two important methods that every mapper should know and use.
Caulking means to apply the special shader "Caulk" (which can be found in the "common" section) to all surfaces that cannot be visited by the players or spectators (e.g. the outside walls of rooms and corridors). Actually, you should work the other way round and change the NetRadiant preferences so that a new brush automatically uses the texture "Caulk" on all 6 surfaces. Later, you should apply textures on the visible surfaces.
The Caulk shader is invisible, so the game engine does not waste time on it. But Caulk faces must be prevented from being seen by the player because they would show the Hall of Mirrors effect. Caulk faces of normal (meaning "structural", not "detail") brushes block the Vis, just like normal textures would. A map in which all unused surfaces are Caulk'd has higher FPS than the same map if all unused surfaces are normal textures. This is one of the two main reasons that the brushwork should be created with Caulk'd surfaces (see preferences tip further up) rather than real textures.
Clipping in general means to use the clip function on brushes to change their shape or size or to split them in two. But when people say that "mappers should use clipping", they are referring to a specific kind of clipping that goes hand in hand with texturing.
Imagine that you're looking at a 4-wall room from the top. Somehow, the four walls have to meet in the corners. A mapper newbie could make the big mistake of having the walls overlap in the corner. Overlapping brushes should really be prevented if possible. The first thing to improve would be to make the decision which of the four walls should reach into the corner and which should stop just where the other wall reaches into the corner, so that the walls touch each other perfectly instead of overlapping.
But this is not how a good mapper would do it. A good mapper would use clipping. So, back to the 4-wall room with all four walls reaching into the corners so that they overlap. Now, all four walls have to be clipped on both ends diagonally (a line from the outside corner to the inside corner). So that the surface visible in the room is shorter than the outer surface. So that the walls touch perfectly in the corner.
Now, if you want to "paint" the room by applying textures to the surfaces that are visible from inside the room (and only the surfaces - don't select the whole brush, we want to keep all unused surfaces as Caulk), you could then use the "fit" function of NetRadiant's surface inspector so that the texture looks like it really begins where the wall begins (as seen from inside the room). Now you see why clipping is such an important method if you really want to use textures properly on your map: If we had the previous version of our 4-wall room where some walls reached into the corner and other walls stopped right at the corner, the results of using the "fit" function would not be as we want them to be. And then you'd start handling complicated numbers like 0.065134 or something instead of just conveniently using the fit function and forgetting about the numbers.
The example of the 4-wall room is very simple, and you could have solved it even more efficiently by just making the four walls stop right before the corner, so that the edges of the walls just touch perfectly. That would still be a proper map. And you could still use the "fit" function on the textures. But this example was just to explain what clipping means and why it is important. On a real map, you would quickly be in a situation where the simple edge-on-edge solution as described here wouldn't work, you'd rather use the diagonal-clip solution.
Again, this was just a simple example. Once a more complex situation is built, the clipping becomes quite more complex. But this is how it should be done to achieve proper results while still being efficient.
Another situation where you would use clipping is if you want to paint several textures beside each other. Obviously, a new brush is needed because every surface can only have one texture. So, you would for example clip the wall in the middle, not so that half of it is removed but so that the brush is split in two. This can be selected in the clip menu of NetRadiant. Then, you can easily apply a new texture on one of the brushes.
This is the second main reason that the brushes should be created with Caulk'd surfaces (see preferences tip further up) rather than real textures. And you should change the NetRadiant preferences so that "clipping uses Caulk" is activated. If a brush is splitted in two or if a part of it is clipped away, one or more new surfaces are created. This preferences setting will make sure that those surfaces do have the shader "Caulk".