Deterministic Finite Automatons (DFAs) and Nondeterministic Finite Automatons (NFAs) have exactly the same capabilities and limitations. The only difference is notational convenience.
A finite automaton is a processor that has states and reads input, each input character potentially setting it into another state. For example, a state might be "just read two Cs in a row" or "am starting a word". These are usually used for quick scans of text to find patterns, such as lexical scanning of source code to turn it into tokens.
A deterministic finite automaton is in one state at a time, which is implementable. A nondeterministic finite automaton can be in more than one state at a time: for example, in a language where identifiers can begin with a digit, there might be a state "reading a number" and another state "reading an identifier", and an NFA could be in both at the same time when reading something starting "123". Which state actually applies would depend on whether it encountered something not numeric before the end of the word.
Now, we can express "reading a number or identifier" as a state itself, and suddenly we don't need the NFA. If we express combinations of states in an NFA as states themselves, we've got a DFA with a lot more states than the NFA, but which does the same thing.
It's a matter of which is easier to read or write or deal with. DFAs are easier to understand per se, but NFAs are generally smaller.
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