Later series of stock are most often described as senior to previous rounds of investment, meaning their terms take precedence over the previous rounds' terms. In some cases (for instance if the round is flat) the liquidation preference can be "para passu", in other words, at the same level as the previous round.
The specified terms for the liquidation preference instructs how much cash the series shareholders may take out before others get paid out. This term is indicated in multiples of the cash that was put into the round (i.e. 1x is equal to one times the amount put in, 2x is equal to two times the amount put in, and so on). And there's one more thing to keep your eye on and that is participation. The terms can be set to either 1) exercise the liquidation preference with no participation, or 2) exercise the liquidation preference with participation. No participation is straight forward. The investor takes their money according to the liquidation multiple specified and is done. Exercise with participation means that the investor gets the money according to the liquidation multiple specified and if there is any left over after all preferred have exercised their liquidation preferences also gets to participate in the distribution of the remaining cash.
Let's take a case as an example:
ABC corp has undergone two financings, an A round, and a B round. The A round has a liquidation preference of 1x and $2M was invested for 40% of the company, the B round has a liquidation preference of 1.5x and $5M was invested for 30% of the company. So if the company now has 1,000,000 shares, the B round holds 300,000, the A round holds 280,000, and the common hold 420,000. The company has had trouble gaining revenue traction and decides to sell to a suitor who wants to acquire the technology for $10M. To further simplify the company has no outstanding debt (which would need to be paid out before the investors) and has no money in the bank and no accounts receivable. Without liquidation preferences the series B shareholders would get $3M, series A shareholders $2.8M, and common shareholders would receive $4.2M.
If both series A and B have a 1x non participating liquidation preferences, then series B would receive $5M, series A $2M, and the common would receive the remaining $3M.
If both series A and B have a 1x participating liquidation preferences then series B would receive $5.9M ($5M + 30% of the remaining $3M), series A $2.78M ($2M + 28% of the remaining $3M), and common would receive the large payout of $1.26M (42% of the remaining $3M)