Attaches to the た-form of verbs and adjectives, or to nouns/na-adjectives with だ→だって. Expresses a concessive condition: 'even if it is the case that...'. Often used in casual speech.
Even if you cry, it won't help.
Even if we go now, we won't make it in time.
Even if it's cheap, I don't buy things I don't need.
Follows a volitional or question word to mean 'no matter how much one tries' or 'however one does'. Often used with いくら/どんなに/何度 etc. Also appears as ったって in casual speech.
No matter how much I ask, he won't listen.
No matter how much I hurry, I won't catch the last train.
No matter how hard you try, what's impossible is impossible.
No matter how many times I tell him, he doesn't listen.
ても is the neutral, standard form for 'even if' usable in formal and written Japanese, while たって is its casual, spoken-only counterpart.
たって spells out the 'even if' meaning explicitly, while って after a past-tense verb is the casual contracted form of the same construction.
Contraction of たとて, itself from the past/perfect auxiliary た + とて (old-fashioned concessive particle). The form だって is the corresponding form for nouns/na-adjectives.