Too few drivers you get long waits or surge prices. Too few riders and the drivers start to disappear...
Network effect is when each user brings additional users (or each user prevents other users from leaving).
For every additional driver, the density of drivers on a map gets higher. When this happens, statistically the closest driver will take X less time to get to you.
Two sided markets are not about having a minimum number of people.
Two sided markets are literally a network effect.
https://en.m.wikipedia.org/wiki/Two-sided_market
The "traditional" network effect is describing one sided markets. But it is a normal economic concept to talk about the two sided network effect as well.
Think of it this way. In a 1 sided network, ever user type A makes it more valuable for other user type As.
In a two sided market every User A makes the network more valueable for User type Bs. And every User type B makes it more valuable for user type As.
If everyone is spaced evenly around the place and there's no congestion, you need four times as many drivers to halve response times. For a while you get good gains per additional driver, but as the numbers increase the marginal benefit tails off. This means a new player with some capital can likely compete (and is probably what the grandparent meant by "saturation".)
In most two-sided markets, the ratio of users on both sides plays a more important role than absolute numbers.
Uber sees this through its financing, application, comms network, drivers, members/subscribers, and political influence.
Transport, comms, data/information, knowledge itself, and land are all classic networks, subject to network effects, and monopoly pressures.
What is Uber's network effect? Most people I know will use whatever app gives them the cheapest ride / will drive for multiple companies.
There might even be an opportunity for a $1 app that tells you which service you should use at any given time/location.