The skills that are Omega-only (past Alpha levels) will grey out and become inactive; they’ll remain your character sheet but they won’t provide the bonuses that they’re supposed to provide.
Skills unlock ships, and also skills unlock modules for you to use (install in your ships and use). So for example you will lose access to Tech 2 ships (cov-ops for example), but will still have access to Tech 1 ships (basic cruisers, for example). However, if you have a cruiser that has Tech 2 guns in it, you won’t be able to get into the cruiser because the Tech 2 guns are installed but you don’t have the skill for them (it’s greyed out Omega only). So you have to uninstall the guns before you can use the ship.
So what Ralph is recommending above is to do some “spring cleaning” as it were, and put away the ships / gear that will become locked out, and otherwise the ships that Alphas have access to, get some alpha-level gear for them.
Because one of the things that gets disabled is industrial / transport ships (you still get access to level 1 of the industrial skill), so your max carrying capacity for “loot / gear” will likely get reduced from 10-15,000 m3 to 2-4000 m3 or so. Which means more trips to Jita.
You also get fewer market trading slots, and only 1 contract slot. So trading / getting gear as an Alpha is a bit more cumbersome.