At some point in a guitarist's career, he or she gets to a stage where they want something more out of their guitar, something a little more complex. Strumming is fine and a great way to accompany yourself while singing, but it can be limiting. For example, if you have just one point of contact (a plectrum) with the strings, it's hard to create complex musical patterns even if we move a hands very quickly.
Of course, some flat pickers are amazing and learn very special picking techniques to 'speed pick', which can be incredibly fast. Doc Watson was such a picker, re-creating traditional fiddle tunes on his guitar, but even he knew that for some songs finger picking was needed. The one huge difference between using the individual fingers instead of a plectrum is that we can pinch two strings together at the same time. This is impossible with a plectrum.
Once we decide to start finger style guitar, there's another choice to be made first which might not be so obvious to the beginner. Finger pickers either just use their bare fingers to hit the strings, or a combination of metal or plastic picks. Others prefer a plastic thumb pick with bare fingers, it's all a matter of preference and playing style, although there are no strict rules about the matter.
Bare fingers make a very soft sound, but the player can feel the strings which tends to increase control and promote a delicate touch. The downside is that the tips of the fingers can get very sore, and at least an hour's practice a day is need to keep the callouses tough and ready to play. On the other hand, picks are a natural amplifier and give a sharper, clearer sound - great for players performing in noisy locations, such as busking in the streets.
It's to understand why some of the classic blues men playing in noisy bars from Texas to the Delta would sometimes use a National Steel or similar resonator instrument in combination with steel or plastic picks. The notes would easily cut through the hub-bub of a noisy crowd of people. Another option is to use your own nails, but your touch should be gentle because they will be worn down very quickly, even if reinforced with lacquer. It's also possible to buy false acrylic nails that are simply glued to the natural nails.
Lastly, the angle of attack for all types of playing preferences are very different, but the necessary changes are easily assimilated. Perhaps the biggest challenge is to use bare skin for some songs, and picks for others. This means that you would need to be very comfortable with both angles of attack and be able to switch from one style to the other at will.