The two are close friends who adventure together and go through many obstacles as a pair, but mostly as a trio (with Morgiana.) At first Alibaba only wanted to become close to Aladdin because of his Djinn Ugo. He wanted his help in conquering a dungeon. However, through the journey, he and Aladdin truly became close friends. The two are very loyal to each other, and Alibaba occasionally feels insecure without Aladdin around to help him. Aladdin often encourages Alibaba to do as he wants to, rather than letting somebody else dictate his fate. Aladdin is also Alibaba's 'clubbing buddy', and they often go to brothels together. At first, Alibaba seems to be a greedy cart-driver with big plans, but the two warm up to each other. While Alibaba's initial intentions were to use Aladdin and Ugo to beat a Dungeon and get a large amount of riches, they quickly became friends and extremely loyal to one another. After beating the first Dungeon, Amon, Alibaba waits for Aladdin to return but, when he doesn't, Alibaba leaves with a note in case Aladdin ever comes back. Currently they are very close friends and fight well together, trusting each other and supporting one another through the trials and battles. Unlike their masters (Yamraiha and Sharrkan), the two get along well. Aladdin admires Alibaba's ability to put himself in danger for the benefit of others and the greater good. He is also Aladdin's King Vessel.
Even after Alibaba's apparent "death", Aladdin never gave up on him and knew that one day his friend would return. After the time skip, he teases Alibaba a bit more but is happy nonetheless that his friend is by his side once more.
In one scene during the finale, after Alibaba gets corrupted, Aladdin tells his friend that he is courageous and means a lot to all of the people he's met. In the same scene, Aladdin finishes his speech by saying: "After all, you're Alibaba, whom I love so much!" While reaching his hand out for his companion.
People portray them in many different ways. Most people interpret them as simple best friends or having a brotherly relationship; this is especially because, in canon, Alibaba gets married to Morgiana. However, a decently large portion of the fandom ships the two, often making shipping art portraying them in different scenarios.
The fandom is divided on how they view AliAla in the context of romance. Most people view it as friendship, but another large portion also see them romantically. However, despite this, there isn't much AliAla fanfiction in the fandom, although there is plenty of fan art on sites like pixiv and ZeroChan.
There are also some people in the fandom who find the ship to be problematic, especially because of the large age difference. With Aladdin being 10-11 at the beginning of Season 1, and Alibaba being around 17, many people see it as potential shotacon and have even produced small groups of fans who hate the ship for that sole purpose.