Odds in gambling refer to either odds for winning/losing or odds that the bet you made shall get you a payout. The difference is the house edge or the player edge.
Take a 4-sided dice. The odds of getting a particular number when you roll a 4-sided dice are 1 in 4 or 3 to 1. Every number has the same probability of coming up. Out of the six probable outcomes only one of shall be the winning result. Odds are generally stated in the following format: 3 to 1 i.e. there are 3 numbers to lose and only 1 number to win, with every number having an equal scope. Odds state a ratio that can also be translated into a fractions or percentages.
Slot machine odds were determined by a number of mechanical devices. Every reel had a certain number of symbols and the odds for the player hitting a said symbol would be 1 divided by the total number of symbols. General arrangement has 3 reels along with 10 symbols per reel. Here the odds of getting any particular symbol on any single reel shall be nine to one.
Each bet payout is set below the probability of winning the said bet. The payout is multiplied by the said probability to give the payback percentage/ bet. When you add them up you get the payout % for the machine.
Modern slot machines are radically different from the ancient mechanical slot machine. The mechanical and physical reels have been replaced by video screens. The mechanical stops that decided the exact spot the spinning reel would end have been also been replaced with RNG's (random number generators). These changes have brought dramatic changes in slot machine payouts and odds.
Physical reels can hold around 20 symbols before it is impractical to be used in slot machines. Physical slot machines can't accommodate higher than 3 reels easily. However video slot machines have no such limitations ad can have 5 or more reels with 100 symbols in each reel.
The RNG can and is also programmed to provide certain symbols a varying scope of coming up and is in no connection with the actual number of symbols. As a result the less probable combinations can be easily programmed. The lower the probability to hit the combination the higher the casino manages to pay as payouts. Progressive jackpots of 6-7 figures may be impossible on mechanical slot machines, but they can be easily programmed into the video slot machine's RNG.