they refer to a champons main job within your team. a damage dealer is pretty much what it says; their job is to hit and hit hard, without much concern for anything else. examples include champions like turvold or ithos, who are almost entirely focused on damage.
control generally refers to crowd control or turn meter control. any champion focused on crowd control will be able to place one of the crowd control debuffs—stun, sleep, fear, true fear, freeze, provoke, or petrification—over the entire enemy team. examples include harvest jack, visix, and scyll. turn meter control champions look at increasing the turn meter of their own team and decreasing their opponents', like lyssandra or psylar.
debuffers are champions whose job it is to land debuffs on the opposing team, whether they be the crowd control debuffs mentioned earlier (now might be a good time to mention, there's a fair bit of crossover between the latter three types of champions and a fair number that are hard to pin into one single category), stat-lowering debuffs like decrease attack or defence, or damaging debuffs like poison or hp burn. negative instants such as buff removal or increasing cooldowns also tend to get lumped into this category. examples include champions like narma, madame serris, and nekmo thaar.
finally, support in this context typically refers to champions who help out your own team via healing, buffs and revival. champions like duchess lilitu, apothecary, or godseeker aniri are all perfect examples of support champions.
in regard to the designated roles on a champion (attack, defense, hp, or support), there's some relation to what postion they will fill in your team, but it's not a hard and fast thing. attack champions will usually be damage dealers while support champions pretty much never will, but beyond that anything's fair game. there are a lot of champions who fulfill multiple different jobs or can change depending on how you build them. an example of the former would be ninja, who is a pretty clear damage dealer but also brings along a really nice crowd control on his a3. a good example of the latter would be someone like hurndig. he has the potential to be a very hard hitter, but also has a lot of good debuffs in his kit so it depends on whether you build him with the focus on attack and crit rate/damage or sacrifice that damage potential to give him more accuracy.