You would create your new environment with the command
\newenvironment{thisismyown}[num]{begin}{end}
where [num] is the number of arguments you want to pass to the environment, and can be omitted if you don't want any; begin is the text that will be inserted at the point that you call \begin{thisismyown} and correspondingly end is what will appear when you have \end{thisismyown}.
As for why you'd want to, the primary reason is if you have some sort of element that you will repeat multiple times -- theorems, problem statements, solutions, Shakespeare quotes, ... -- and want them all to be formatted in the same way. By putting the formatting into a new environment, you make your document source more readable and can easily change the environment in a single place to update all instances of it throughout your document.
For example, perhaps you are typing up an assignment and want to have an environment to define how your answers will look. You could use something like this:
\newenvironment{question}[2]{
\noindent\textsc{Question #1}:\begin{quotation}\textit{#2}\end{quotation}
}{
\hrule\vspace{2em}
}
...
\begin{question}{1}{Solve for $x$.}
The answer is, $x=42$.
\end{question}
Every question will be nicely formatted to have a label in small caps, numbered by the first argument and restated by the second one. You then place your solution inside the environment, and when it ends you get a solid line across the page and some blank vertical space. Of course, you could also use customized counters to keep track of the question numbering for you, but that's a whole other answer...