Why some people like Minions?

One of the reasons people watch cartoons is to laugh. Minions are considered funny by many people and they can easily make them laugh.

According to psychologists cute things can easily become popular because our desire to care for little things can make us more attached to them. This is also one reason why Cat memes are popular.

According to psychologists unexpected rewards motivate people and keep them hooked.

There are lots of minions with each having his own different personality. The diversity in personality makes the minions appeal to a broader range of people.

According to psychologists people find kids cute because of many reasons that include their big eyes. A person can see a minion and unconsciously recall the image of a baby.

Yellow is color known for it's ability to catch attention. Yellow is connected to optimism and it can give people a pleasant feeling when used properly. (See Why are bright colors eye-catching?)

Minions speak a language of their own. This makes it possible for all people around the world to watch minions without worrying about language barrier. 

Minions sometimes use words from different languages. This can help people around the world relate to them.

Minions do what they feel like without caring about anything. This makes them seem more funny to some people.

After their widespread minions became familiar faces even to people who didn't watch their movies. According to psychologists people tend to favor familiar things over others. (See Why do we like familiarity?)

Because minions don't speak a certain language and because their faces are expressive they can fit in so many different memes. This is one reason Minion memes are popular.