MaceyNeil: I believe what is meant is the progression from easy start to hard mode all bosses defeated glory.
There are good wiki's on the bosses, but let me break it down for you.
There is no level to your character as an integer(number); that is not to say you do not effectively 'level up' as far as the game is concerned, but i'll come back to that later.
The game starts in a normal biome with easy areas and different biomes can provide extra challenges.
Jungle biomes have bats that can be annoying with a wooden sword, corrupt areas have persistent floating style enemies and even underground there are biomes for example there is a spider cavern where the prominent features are hanging webbed corpses, web and of course spiders that crawl along the walls.
As far as initial biomes go the MOST difficult 'level' is the hell biome generally about a depth of 3250feet down i believe and running completely along the bottom of the world.
There are of course the bosses.
The first is the eye of cthulu
eater of world/brain of cthulu
Followed by Skeletron
Then Wall Of Flesh, which is not to say there are not other bosses but generally this is the order in which people face them.
Mainly because the game becomes significantly harder once you defeat the wall of Flesh (see the wiki for Hardmode).
After defeating the wall of flesh hallow and taint will spread like wildfire both nasty biomes to be in moreso with the fact ALL enemies become much more of a challenge.
A lot of what scales the difficulty though as i have experienced and researched is your stats, your life points and mana seem to indicate the sort of major encounters you ahem encounter.
Largely though difficulty is set by what can spawn in the biome and enemies encountered are of that biomes set type; with the only real difference is the almost unavoidable progression to hard mode.
As far as the player is concerned though with any game system with a hero that is suppose to get stronger and in actuality never accomplishes this due to threat scaling (a bit like superman growing up to suddenly find himself due to his hero status always dealing with other people from krypton instead of meager human threats) the games difficulty is largely dependent on luck with a tiny bit of self determination in what you craft because you will always be a loose jumble of meat bits waiting to happen with only the careful selection of gilded brick a brac there to keep things all together.
Progression of brick a brac largely is about increasing your mobility, defense (easily seen by the copper iron silver gold (amethyst, topaz ,emerald, saphire, ruby, diamond for some things) increments) style of attack (+ of course damage) & increasing stat bonuses (or gaining efficiency in their use such as regeneration, chance not to use ammo, +40 mana, etc.)
I hope this has been comprehensive enough, just remember the games not going to tell you where to go and what to do; you are going to have to decide you want to dig into hell defeat the wall of flesh and deal with the consequences of tainting every last square of rock dirt or sand.
I would also like to add Queen Bee in the pre-hardmode underground jungle, while she is not necessary to kill she does drop some sweet loot