Jellal and Erza have known each other since their childhood. They worked in the Tower of Heaven-a magic item that allows any person to restore life upon someone who is deceased. Jellal had become mad and since Erza sincerely loved him and cared for him she wanted to snap him out of it for his own good (this was in tower of heaven arc). Jellal had been imprisioned for acting selfishly and believing to revive Zeref and Erza had cried her eyeballs out when she realized he would be locked up for the rest of his life. During the Grand magic Games Jellal had confronted erza and told her he escaped prision with the help of Gray's friend Ultear. Erza and Jellal have a conversation reminscing. In the process they almost share a kiss but Jellal interuppeted it by lying about having a fiance-but ofcourse Erza saw right through him. Jellal didn't want to hurt her again. Jellal is her love interest and Erza often thinks fondly of him.
Natsu is another one of Erza's childhood friends since she became a member of fairy tail after escaping from the tower of heaven. Erza is like a tough love sisterly figure to Natsu-and Natsu is the litte brother that is still growing and learning. When they were younger Natsu and Gray would constantly fight for no moral reason and Erza would break them up and all three of them would start chaos(this is still happening in the future). Although Natsu is reckless, challenges and atagonizes her, him and Erza maintain a healthy relationship. In some battles Natsu was save by Erza and in some other battles vice versa.
Gray and Erza's relationship is something like Natsu and hers. The two have known eachother since childhood and unlike Natsu, Gray is not as hot headed and isn't so prone to test her temper as well as pick fights with her. The two are good friends and are always there for eachother when one of them has a problem they need to triumph. When Erza first came to the guild when they were younger Gray had a different point of view of her. He didnt eaccept her as a comrade then because she use to keep to herself and ignored him. When he saw her cry he later on accepted her and the two maintained a health brother and older sister relationship like Natsu and Erza's.