If you beat the dealer’s hand in terms of value (while remaining under 21), you win. When the bets have been down and you’ve drawn as many cards as you deem necessary, the dealer will play their hand to determine the benchmark. Higher value hand with an additional card, or to stick with what you’ve got in the hope of winning. It’s up to you to decide whether you want to push. The dealer has less room for maneuver and plays in a more straightforward way, often sticking automatically at 17s and above. Depending on their hand - to draw another card, or to stick with what they’ve got.
Players have the choice to hit or stand with every rotation until the game is complete. The game moves in turns, with players to bet on the strength of the two card hand they are deal. All that matters is that your hand has a higher value than the dealer’s hand, without going over the 21 threshold.
So if the person to your left has a better hand than you, it’s irrelevant. Each hand takes place between the dealer and the individual player only. While it is common for blackjack games to be playing with multiple players around a table.