Very hard to say what the actual changes are without looking at the specifics of Russian nuclear protocols (which nuclear countries do not generally share much, preferring to remain ambiguous).
Russia's forces, like US ones, are capable of reacting to a first strike and thus are capable of operation without being "warmed up". This is true for ICBMs and SLBMS (sub-launched).
However, at the political level, it is very clear what message is intended: "Russia is a nuclear state and don't you forget it". Nuclear alert levels were a ritualized signaling mechanism during the Cold War. Like a dog growling and raising its hackles it is meant to signal that it might bite. Not that it will bite, but that it wants you to know it is ready to (this is akin to moving the US's DEFCON levels, as Fluidcode points out)
Nuclear war is so dangerous that it is critically important to have a variety of signals to indicate intents and especially the level of threat you perceive from others or want to signal to others. Alert levels are part of that.
What it's not is an indication that Russian forces are prepping for launching a strike. Those wouldn't be broadcast in advance.
Most nuclear forces have been "off-alert", for whatever actual meaning that has, since the end of the Cold War. This is a spike back up.
If you go back earlier in time in the Cold War, nuclear readiness was more gradual and had actual meanings, with aircraft needing to be loaded and possibly being put on station near the enemy territory. Earlier Soviet ICBMs were liquid-fuelled and needed considerable prep before being ready for launch. This is not the case anymore however. You do probably have things like bases being locked down and personnel being pulled back from leave.
Putin already reminded us that Russia is a nuclear state in his original speeches on the 23rd. At one level, this is, usefully, reminding the more gung-ho of Western politicians that "boots on the ground" or engaging NATO air forces directly over Ukraine is a non-starter. What got us out of the Cold War in one piece is never to risk direct NATO-Russia combat.
This something Biden, correctly, identified back when he advised US citizens to leave.
Biden made the remarks in an interview with NBC News' Lester Holt, who asked him what kind of scenarios would prompt a U.S. rescue mission, if Russia invaded.
"There's not [one]," Biden said. "That's a world war — when Americans and Russians start shooting at one another, we're in a very different world than we've ever been in."
At another level, Putin would no doubt be thrilled if the West stopped supporting Ukraine altogether because the more timid amongst our politicians lost their resolve. However, this risks being another miscalculation - whatever Russia can do to NATO, NATO can do to Russia and Putin is losing world sympathy by the day with his antics. China, for one, would be horribly impacted if Putin managed to trigger a full on war. MAD is just as suicidal to all parties now as it was 30 years ago.
To give an example of nuclear alertness level influencing a crisis, Israel loaded their nukes during the early days of the Yom Kippur War, when they were not doing well. And the US, which before had dragged its feet on helping them, immediately flooded them with military aid.
Or during the Cuban Missile Crisis:
US alert level raised
Adlai Stevenson shows aerial photos of Cuban missiles to the United Nations, October 25, 1962.
The US requested an emergency meeting of the United Nations Security Council on October 25. US Ambassador to the United Nations Adlai Stevenson confronted Soviet Ambassador Valerian Zorin in an emergency meeting of the Security Council, challenging him to admit the existence of the missiles. Ambassador Zorin refused to answer. The next day at 10:00 pm EDT, the US raised the readiness level of SAC forces to DEFCON 2. For the only confirmed time in US history, B-52 bombers went on continuous airborne alert, and B-47 medium bombers were dispersed to various military and civilian airfields and made ready to take off, fully equipped, on 15 minutes' notice.
Further readings:
Alert Status of Nuclear Weapons - Federation of American Scientists
Despite concern about realerting effect, both
US and Russian escalation strategies rely on
significant realerting to signal and boost
nuclear postures in a crisis.
Alert status of nuclear weapons - AIP Conference Proceedings
Since end of the Cold War, nuclear alert rates have been reduced in several ways:
• Strategic bombers were taken off alert in 1991.
• ICBM warhead loading reduced (United States); New START treaty included ICBM MIRV ban but was
abandoned in favor of ballistic missile defenses against rogue states.
• SLBM warhead loading reduced (United States).
• De-targeting initiatives: ICBMs/SLBMs targeted at open ocean areas during peacetime (note: de-targeting is
not dealerting).
• Non-strategic forces taken off alert. Most warheads destroyed but remaining placed in central storage. Some
still deployed on bases near launchers (US bombs in Europe; French cruise missiles).
Note that the AIP publication also uses the term to indicate weapon readiness, where they say that Russia and the US both have about 20% of their nukes ready to fire on short notice. That's likely not what this is about, short term. This is about personnel, not gear:
Putin has ordered the defence minister and the chief of the military to put nuclear deterrent forces in a ‘special regime of combat duty’.
Finally, in a some-dude-on-Twitter-said vein, I found this when I tried to compare US Defcon levels to what Russia is up to:
Like US DEFCON levels, Russia has a number of readiness levels:
- CONSTANT
- ELEVATED
- MILITARY DANGER
- FULL
Putin ordered nuclear forces to ELEVATED level today. Concerning but not cause for panic yet
(Where 1. would be lowest, as opposed to the US's DEFCON 1 being the worst and DEFCON 5 being "no worries"?)
DW has picked these levels up as well, but is not sure where Putin's "special level" sits.
"The expression he used to indicate some heightened state of alert does not exist in Russian military manuals," Eggert, DW's Russia affairs analyst said.
There are four levels of alert in the Russian military, he explained. Those four levels are: regular, heightened, the threat of war and full or complete.
"Nuclear forces are pretty much always on heightened alert," Eggert noted.