SSBN - A nuclear-powered, ballistic-missile-launching submarine. Also called a "boomer" by Americans and a "bomber" by Brits.
SSB - Conventional-powered, ballistic-missile-launching submarines. The US, UK and France never built any of these, but both the USSR and China did - though not very many.
SSG/SSGN - Guided-missile submarines, with or without nuclear power. They carry large stocks of cruise missiles, intended for attacking either ships or land targets. Most of the remaining ones are Russian, and designed for anti-ship warfare, though the United States has converted four SSBNs to SSGNs for land attack. The missiles carried can have nuclear or conventional warheads, very often a mix of the two.
SSN - A nuclear-powered submarine. These are generally "hunter-killer" submarines, designed to track and, in times of war, destroy, "boomers" (as well as aircraft carriers, other ships, other subs and land facilities through cruise missiles, though the Russians had a policy of using nuclear torpedoes for attacking coastal cities in addition to enemy fleets)
SSK- A conventional-powered submarine, with a long range. Used more by the USSR than the US. Newer, top-of-the-line models are quieter and cheaper than nuke boats, but are much slower. Older ones are just cheaper. These generally aren't designed for nuclear weapon delivery, but as with the SSN, nuclear-tipped torpedoes were for a time used by the USSR and may still be in Chinese stockpiles.
ICBM - Inter-Continental Ballistic Missile. The sort you can launch straight up in the air from North Dakota and hit Moscow. Developed alongside space technology, such missiles literally orbit the Earth (for up to half a complete orbit) while in flight. There is little to no practical difference between an ICBM and all but the heaviest orbital launch systems, and indeed several launch systems are barely-modified ICBMs (the American Atlas rockets used to launch Mercury and Gemini capsules are probably the most famous instances).note Hence the brouhaha about the North Koreans with Nodongs testing the Unha launcher—although there's little doubt that the North Koreans really do want to launch satellites with it, there is also little doubt that the Unha is exactly the same thing as the Taepodong-2 ICBM, which if successfully tested would give North Korea the ability to strike anywhere on the planet.
SLBM - Submarine-Launched Ballistic Missile. Generally smaller, with a shorter range. The advantage being that their missile bases are mobile and stealthy.
MRV: Multiple Reentry Vehicle. Exactly What It Says on the Tin. Distinguishable from MIRVs (below) by the fact that the warheads are not independently targeted, they all fall towards the same target albiet with a bit of a spread. Hence, a missile with a MRV can still technically only hit one target.
MaRV: Maneuverable Reentry Vehicle. Essentially a ballistic missile whose warhead can maneuver during the terminal phase and a portion of the mid-course phase. The purpose is to make interception attempts more difficult OR increase accuracy.
MaIRV: Maneuverable Independent Reentry Vehicles. Really just the above combined with the below.
MIRV - Multiple Independently-targettable Reentry Vehicle. A nifty way of killing lots of targets with one missile - it deploys multiple warheads on the way down. Many will probably be most familiar with this through various video and computer games. Basically, the nuclear version of a 12-gauge shotgun shell with the birdshot being individual nukes.
Kt and Mt - Kilotons and Megatons. A measure of how big a bang we're talking about, expressed in the equivalent amount of TNT. One Kt equals the bang of a thousand tons of TNT (hence kiloton), for the scientifically minded, this is defined as 4.184 terajoules. A megaton is equal to the bang of a thousand kilotons, or a million tons of TNT (4.184 petajoules). Note that you do not need a nuclear weapon to measure explosive force in KTs or MTs, or the inverse for that matter - the Davy Crockett's warhead was measured at 50 tons - yes, just tons, no prefix. On the other side of the scale would be gigatons (Gt). No real nuke has ever been built that would be rated in gigatons,note thankfully, but it turns up in sci-fi fairly often, and in real-world assessments of the energy released by asteroid strikes.