Like most of the students at Hogwarts, Hermione found Snape very mysterious and frightening as he is very strict teacher, she also thought Snape was the one searching for the Philosopher's stone and intended to hurt Harry. However this was proven false, despite this Hermione doesn't fully trust Snape.
Throughout her years at Hogwarts Hermione would be taught by Snape and would excel in his lesson, however due to her always answering his questions whether he asked her or not, he finds it somewhat annoying.
Despite the mistrust she has in him, it seems she does at east care for him and she was shocked and cried when he died - Snape also showed some care for his student as when someone called her a "mudblood", he demanded that word not be used.
Snamione is surprisingly somewhat popular in the fandom, it is shipped due to their relationship over the years and fans seeing Hermione being the one to bring out the good and light of Snape, they see her bringing Snape out of the darkness and for him to love once more.
The ships falls into the popular "Teacher/Student" trope, however unlike most ships of the trope, this one has a bigger age difference which has put off many fans, however the canon relationship of Nymphadora Tonks and Remus Lupin has a big age difference, so there are fans whose the Snamione ship as acceptable.
On AO3, the ship is the second most written ship for Snape and the third most written for Hermione.