According to secular American law a person can be legally blind even if that person is able to see to some small extent. I'd like to know what the halachic definition of blindness is. Is it someone who 100% cannot see anything at all or does it follow any other parameters?
The extent of ones blindness very much depends on the context. There are discussions of the obligation of blind people in terms of positive/negative mitzvot as well as d'orayta and d'rabbanan.
Rashi translates 'סומא' as 'סגי נהור' (Bava Kama 87b), meaning that he cannot see light. However, this is a metaphoric/stylistic phrase since it really means the opposite. It is therefore difficult to extract a precise meaning from these two words.
Tur (Orach chaim siman 53) says that a blind person can 'yored lifnei ha'teivah', as long as he doesn't read from the Torah by heart. This suggests that such a person cannot see the words he is reading.
Tur (Choshen mishpat siman 7): "blind in one eye is kosher to give judgement. But blind in two eyes he is pasul".
Shulchan Aruch (Choshen mishpat siman 35:12): "Blind in two eyes, even though he recognises voices and people, and his testimony matches up, pasul".
Shulchan Aruch (Orach chaim siman 298 seiff 13) says that a blind person doesn't make a beracha on the candle of havdalah and explains (Magen Avraham), that he needs to gaze at the light, implying that only the blessing on the fire he cannot say, whereas the other berachot he can.
The gemara in Chagigah (2a) brings a practical difference between sight with one eye in comparison with two:
סומא באחת מעיניו פטור מן הראייה שנאמר (שמות כג) יראה יראה כדרך שבא לראות כך בא ליראות מה לראות בשתי עיניו אף ליראות בשתי עיניו
So it seems that blind in one eye is enough to exempt you from (at least) this mitzvah. It is interesting that this is for the 'reiyah' (lit. 'sight') offering. I don't know whether the gemara means that (in this case) 'as long as you have partial sight that is considered 'reiyah' for this mitzvah' or not. I am not sure whether this is applicable in all cases of סומא
It therefore seems that there is a spectrum of blindness, ranging from partial (light) sight, without recognising letters, to sight in one eye, to no sight in either eye, etc. Each with their own status in different contexts.