They're different conjugations of the noun blomma. In swedish you have to conjugate nouns in order to make them agree with the other components of the sentence. We do not for example have a "the" like English instead you conjugate the noun.
So the base form or whatever you should call is blomma (using this as an example as you seem to know this word)
If you want to say THE flower, you have to conjugate the word.
In this case it becomes blomman.
blommor is several flowers, in the indefinite form.
you would use this form for talking about flowers in general, as in "I like flowers", "Jag gillar blommor".
blommorna is the definite form, that is "the flowers", as there is no "the" in Swedish, the noun is instead conjugated into blommorna.
Now the rules are tricky for me as a native speaker to explain, as I do not consciously "know" the rules, I just blindly follow them as I learned Swedish from mere exposure rather than by learning the grammar rules. But I'll try;
When you want say "the flower" (blomman) or "the house" (huset) in Swedish, you have to conjugate the noun, as I said. When conjugating a noun it is useful if you know whether to add En or Ett (a, as in a house) before the word. This is sadly not as simple as it is in English. In English you decide on whether to use a or an depending on whether the word starts with a vowel or a consonant, with very few and logical exceptions. In Swedish there is no sure way to tell or some magical rule to follow, it is kind of like French where you just have to learn which one you should use. Although when you speak the language fluently you'll be able to guess, because if you use the wrong one it'll just sound really off.
So once you know whether to use en or ett, it'll be easier to know how to conjugate the known;
En blomma -> blommaN
En stege -> StegEN
Ett hus -> husET
Ett bord -> bordET
En stol -> stolEN
If you use ett it generall ends in "et" or at least with a "t" if en is used it ends with an "n" or "en". whether it is "en" or "n" or "et" or "t" depends on if the word already ends in a vowel... I think.
The plural forms are really tricky for me to explain because when I try to come up with some kind f rule for it in my head, I find myself realizing that it's not really possible (for me at least).
Okay, so I I'm pretty sure you're even more confused than when you started reading my answer, so my suggestion to you is that you pick up a grammar book or ask a teacher or just listen to other Swedes speaking, and read a lot of Swedish literature and the puzzle will slowly fall into place. Exposure is key, trust me, that's how I learned English and I'm also currently learning Japanese. The more you expose yourself to a language the more you will understand.
You asked a very good question though, I must say! You go up to any Swede and nobody will be able to answer this, because we just do not know ourselves ... Unless they're a linguist or something.
Native Swedish speaker.