In order to explain what enrichment is, it's important to consider what a ChIP-seq experiment actually is.
A ChIP-seq experiment is performed to determine where a protein of interest resides on the DNA. In order to perform this experiment you need to have some way of immunoprecipitating (IP'ing) the protein of interest. Sometimes you have an antibody for the protein of interest i.e. a subunit of pol II. Other times, if you don't have antibodies for the protein of interest you may engineer the protein to be fused to a small number of amino acids that you do have an antibody for i.e. TAP-tag, Myc-tag etc. Either way the protein that you expect to bind to DNA will be able to be IP (Hurray!).
Now when performing the IP, you would first incubate the antibody with your cell extract which contains protein, nucleic acids, and other parts of the cell that can go into solution (just think of this as the cells insides that do not precipitate out earlier in the experiment like large debris/cell wall material). So now you have antibody associated to the protein of interest (which is also hopefully associated to some DNA too) but how do you separate the antibody-protein-DNA complex from the rest of the extract? You add protein-sepharose or magnetic beads which are relatively heavy and the antibody can attach itself to. After incubation you can spin the beads and thus the antibody-protein-DNA complex down. You would then wash it off to rinse away everything but your protein which is still attached to the antibody-bead complex. Later you can add a solution to separate this complex then isolate the DNA and you now have DNA that the protein of interest was recruited to.
However you have a problem. The beads you use, are porous and random fragments of DNA and DNA-protein complex can fit in. So when you isolated your DNA-protein of interest you also had some background. So as a negative control we separately perform the ChIP-seq experiment without the antibody, or without the tagged version of the protein. This will isolate the DNA that is non-specifically isolated. So to get back to your original question, enrichment is Reads from the IP divided by Reads from the background IP sometimes called Mock IP or Untagged IP. Having said that, sometimes people just use genomic DNA isolated in the ChIP-seq experiment that has NOT gone through the IP process as a background control ("input"). Therefore input can be a negative control for all steps except for non-specific interactions with the beads during the IP.
Summary:
Enrichment = IP reads / Background Reads (mock IP or untagged IP or input)
I'm not going to go through every figure you just posted, but as far as interpreting these results goes I will give you some pointers. This paper appears to have performed 8 ChIP-seq experiments for different histone modifications and 1 ChIP-seq of pol II in Myoblasts and Myotubes. They had some a priori knowledge of what genes were up-regulated, down-regulated, always or never expressed in MT. For each composite plot they used the expression data to isolate only those genes for each line. The higher the enrichment the more of that protein is present relative to that location on the TSS. And the reason why you see the broad peaks surrounding the TSS for the histone marks is because that is where the -1 and +1 nucleosomes are.
