Well, firstly you had the Present Tense. All the forms that you learned (je, jem, jemy etc.) are imperfective. Their infinitive form is "jeść".
But almost every verb has also a perfective counterpart. That means that the verb already implies that the action was finished. She has eaten a crab 'succesfully'. The perfective verb is "zjeść". And the right form here is "zjadła" (jadła would be imperfective, like 'has she ever eaten a crab').
How do you distinguish in Polish between 'she ate a crab' and 'she ate crab', that is, how do you distinguish between eating a whole crab, and some crab?
I guess you could use a word for "some", i.e. "trochę kraba". But most probably, you wouldn't distinguish.
Anyway, added "some".
"jadł-" is the singular Past stem of verb "jeść" (to eat). Compare 'to have': "mieć" -> "miał-".
"zjeść" is the default perfective form of "jeść" ("jadła" -> "was eating/ate", "zjadła" -> "has/had eaten; ate") implying that the action was completed (she ate a/the whole crab).