Why would one have "waves" in each stage of a tower defense game?

From my experience with the game (Plants vs Zombies) I would say it's a design decision to make the game more accessible, smoother learning curve and a more engaging experience.

Each level (as far as I remember) introduces new weapons, playing techniques and unsurprisingly new zombies, my take on this:

• The designers intended to let you learn and understand how the new techniques work before introducing a harder wave of zombies. This will let you feel more in control of the game, other than splashing tons of enemies and weapons in your face and let you figure it out. The very opposite of what Dark/Demon Souls do, which is one of the reasons why they are considered "hard", they simply let you figure it out.
• This will let the player be prepared physiologically for the next wave, this is not only about learning the game. But also about being engaged. For example a lot of games will give you those hints about a Big enemy coming next (hints: could be music, sound effects, or level design) this will always make you want to see what is coming next, and play more!
• It gives the player a feel of progress.
• This might not be the best thing a hardcore gamer wants in a game. But given the game's success, I would say it was the right decision. At least for the intended more casual audience.

There are a few reasons I can think of. I'll answer this based on the tower defense genre and not just Plants vs Zombies (which of course copied the basic TD formula).

• Setup - Players need time to buy and place new towers. Some tower defense games stop towers from shooting while they upgrade, making the wave break indispensible for tactics. If the player's tower setup is not working for this level's enemies, the small time between waves allows for selling and building of different towers.

• Bonus - Many TD's enable the player to send upcoming waves early. There is generally a bonus for doing so, whether immediate or not. For example as money during the level or just extra points after winning. This would encourage the player to develop a strategy that allows them to send more waves early, further adding to the fun and replayability.

Also, the super wave at the end is something many (if not most) other TD's do as well. It's like any other game that has a boss at the end of the level. You'd better be prepared for it or the rest of the level was all for naught!

In Plants vs. Zombies the game spawns zombies continuously throughout the stage while also having two big waves per level: one at the half way point and one grand finale.

To me, the biggest reason for these big waves is to provide dynamic peaks and troughs in the gameplay. Peaks produce an emotional response that boosts the player's adrenaline and give them the sense they are overcoming a big challenge. "Troughs", or the lulls in between waves, give the player time to mentally relax before the next big wave. This peak/trough dynamic is a lot more exciting and engaging that just a steady, uniform, or slowly increasing spawn rate.

I think the reasons for this are of a much simpler nature: letting the player know how much longer they need to survive and allowing them to react accordingly. For example you know that the next wave is the last wave which will be harder than the previous ones so you pay extra attention towards improving your defenses.

Unless you are making a horror game it is never good to leave the player in the dark about what awaits him. Else it can be a source of frustration, and frustration is not good. The player might think the game is unfair and stop playing it.

Also bunching up enemies distributes the damage your towers are dealing differently. If the enemies are spawning at a fixed rate, there is no accumulation of enemy groups that create interesting gameplay events. If everyone moves at a fixed rate, the level is very predictable. After you've seen the first two enemies get destroyed - you already know you've won and the level will feel repetitive.

If you bunch up the enemies into groups (and with different speeds) then the zombie who takes damage from your towers keeps changing while they move - in effect moving the weaker zombies to the back when they've taken damage.

Waves and the lulls in-between provide a few advantages to the player.

1. They provide more variety of play types. In PvZ, this is embodied by elements like the peashooter vs. cherry bomb: the peashooter can beat 10 enemies separately, but if they are in a clump, you need AOE. By varying the type of challenge, they prevent a single optimal strategy, and let us have a more interesting experience. (extra credits has an episode on this here)

2. They provide time to prepare for the next challenge. In plants versus zombies this is important due to the cool-downs on different plants, you can't build them all at once even if you can afford it. The lulls also allow planning, increasing the strategic value of the game.

3. They provide more sentiments of victory per level, as you get a feeling of victory every wave, instead of only at the end of the level. They also give some adrenaline when a near miss occurs.