Basically, steeping, partial mashing and mashing are steps in the home brewing progression to all grain brewing. It is important to note that although there are progressive steps you can take leading up to all grain brewing, all grain brewing isn’t the “end all” for all brewers. While many brewers get deep into the hobby, and desire working towards all grain home brewing, many brewers are happy to remain at some point along the spectrum, and never progress to all grain. And this is completely fine, this hobby allows for the individual to find what works best for them, and to be able to produce great beers no matter where you brew within the home brewing spectrum.
Each step allows the home brewer to exert more control over the flavor of the beer. Steeping grains allows you to add flavor that you won’t get with extract. Partial mashing or mini mashing allows you to introduce base malt from grain, and mashing is all grain brewing. Each step will allow you to try new and different variables. It is very much like cooking—learning about new ingredients and spices allow you to create a new variety of dishes.
Here is a quick rundown of the home brewing spectrum: most brewers start with beer kits, which is extract brewing. They get hooked, but want to be able to exert more control over the final flavor profile of their beer. The next stop would be to add steeped specialty grains to their extract brews. From here, the next step up would be partial mashing, in which you replace some of the malt extract with the base grain. Finally, you have all grain home brewing in which you brew completely from grains and use no malt extract.
Again, it is up to you is you want to try all of these styles, or stick with just one. You don’t necessarily have to start with extract, although it is a good idea to get a few batches under your belt to better understand the basics of the home brewing process before trying to jump into all grain. No matter what, you are free to experiment and see which way works best for you—and best of all, along that journey you will enjoy some great homemade beer!