NMR stands for No Moves Recorded, which happens when someone doesn't submit orders for a phase where they have orders to submit. When someone NMRs, all their move orders for that turn are holds, all their build orders are to postpone the build, and all of their retreats are disbands. If they have to destroy units, the site picks units to destroy for them.
CD stands for Civil Disorder, which is when all of your country's units are set to hold, your status is set to left, and someone else is able to join the game in your place. Typically, a country will go into Civil Disorder if they miss two turns in a row. However, if your game has NMR protection set to default, any NMR during the first year (this can be changed by editing "turns", which refers to the number of half-years where NMR protection will apply) will cause the country to go into civil disorder and cause the phase deadline to be extended so a new power can join (this is what "delay" refers to).
Typically, it's considered bad etiquette to NMR/CD, even if your country is doing badly. It also negatively impacts your Reliability Rating (a measure of how good you are at submitting orders on time), and if your Reliability Rating gets too low, you might be barred from joining some games.