These people are pattern chasing, or pattern spotting. Quite simply they are looking for patterns in the outcomes of the hands. You may ask why. There is no rhyme or reason to use pattern spotting as a baccarat strategy, it's simply superstition. So although you may see everyone around you marking down numbers, take it as entertaining company, but don't be fooled into participating.
Card counting is another technique that people attempt to utilize as a baccarat strategy.
This method is usually associated blackjack, and involves keeping track of cards that have been played from the shoe in order to gain an advantage against the house. This sounds awfully promising considering the nature of baccarat. As more cards are played from the shoe, the more you know about the cards that are left. But even though cards can be shown to be mathematically favorable or unfavorable, the effect is miniscule. Unlike blackjack you can't alter your bet mid-hand.