They are like small computers
Smartphones have evolved to become more like small computers that can do many of the tasks computers could do. A person could check his email, do his work, install applications and do many other things using a smartphone.
A wide range of functions
Smartphones have a very wide range of functions including being internet accessing devices, gaming devices, music playing devices and many other things. This made smartphones appeal to a large number of people.
They are more portable than computers
Smartphones are much more portable than computers. Many people started using phones instead of desktop PCs and laptops.
They are cheaper than computers
Smartphones provide a wide range of models. Many of those models are much cheaper than a personal computer. This motivated many people to buy smartphones instead of new PCs.
Smartphones helped people become connected to the internet 24-7. Since the internet is highly addictive, many people got motivated to own a smartphone.
It became the new norm
Smartphones became popular to the extent that they became the new norm. People who don’t own a smartphone usually find themselves isolated from others and unable to communicate with them properly. (See Why smartphones are getting bigger?)
The picture taking boom
The social media boom, the selfie boom and the mobile camera boom all motivated people to buy smart phones in order to take part in this movement.
Ease of access
Even people who have personal computers find smartphones much easier to access. A person could, for example, watch a video on their smartphone in order to save the effort of getting hold of the PC and turning it on. (See Why do people take selfies?)
They became connected to social status
In addition to their other uses, smartphones became an indicator of social status. Many people buy iPhones for example in order to display a certain social status.
Applications extended their functionality
Applications extended the functionality of smartphones, thus making almost everything possible. Any person can thus buy a smart phone and customize it with apps to fit their specific needs.
People carry them all the time
The fact that people carry their phones 24 hours encourages them to use them all the time. The increased usage of smartphones made them addictive and more popular.
Addictive apps and addictive social networks have made smartphones more popular as more and more people bought phones to be able to use those apps.