The surrender option is not a well-known rule at Blackjack because it is not offered everywhere, live or online. Most players do not use it or do not know how to use it when they play online Blackjack.
Surrender means that you can decide to forego the hand once the first cards are distributed. This is useful when you have very bad cards versus the dealer and a low chance of winning. But there is a cost for doing that, as you must give up half your bet.
If you are likely to lose, better lose half the bet than the entire bet, right? The question is when does it make sense to surrender. And the answer is rather simple:
Surrender when you have less than 25% chance of winning. This works as follows. Assume that you bet $10. On average you win $20 25% of the time, so your expectation is 25%*$20 = $5. Which is half the bet. So if you have less than 25% chance, it is better to simply surrender you hand, as the odds are so bad it will cost you more to stay in the hand.
Surrendering should only occur in a few cases, as it is very unusual to have such bad odds. The only hands where this is happening are 15 and 16, but it also depends on other factors, such as the dealer's up face card. Here are a few tips on when to surrender, assuming the dealer stands on 17.
When you have 16 and the dealer has 9 or higher, you should surrender. The only exception is if you have a pair of eights, in which case you should split.
When you have 15, only surrender versus a dealer's ten.
You could add a few tweaks to these rules if you do card counting. For example if there are not many tens left in the deck, you can hit with a 16 versus the dealer's nine, or with a 15 versus the dealer's ten.