Black-Scholes is one of several pricing models that uses six variables to determine the theoretical value for an option. You mentioned five of them. You did not mention a dividend so it is assumed that there is none.
What's lacking in your question is an understanding of what a call option is, namely the right to buy an asset an agreed price on or before a particular date. If the option is European style (most indexes), they can only be exercised at expiration. American options (stocks, ETFs) can be exercised at any time.
In your example, the buyer of the call pays $234 (quoted at $2.34 per contract) for the right to buy the underying at $100, if so inclined. Should he prefer not to own it, he can sell the call at any time in the option market, perhaps for more, perhaps for less.
Puts are the mirror image of calls. The owner has the right to sell the underlying at the exercise/strike price, if so inclined.
In both cases, the owner of the option has the right. The seller has the obligation.