Constraints on a symmetric pareto allocation under uncertainty
The idea is that since agents are ex-ante identical, they should have the same (ex-ante) expected utility. 

Ex-ante identical means that even the agent does not know what's his type until resolution of type at date-1. Because they have the same preferences each agent's consumption profile must be identical. And the analysis can then focus on symmetric equilibrium.

What symmetric means, as explained in the footnote, is that the consumption profile must be identical. The consumption profile $(C_1, C_2)$ represents the consumption for the agent at date 1 (if he is type-1) $C_1$ and the consumption for the agent at date 2 (if he is type-2) $C_2$. Otherwise stated $(C_1, C_2)$ does not depend on the type and each agent has the same $C_1$ and $C_2$. Since the types coincide with the date it's a little bit trivial but it really says nothing more than that.

For the constraint, there is a mass-1 continuum of agents, each endowed with one unit of wealth, so the total wealth is 1. Then from that total wealth an amount $I$ will be invested in the productive technology whose return is $R$ per unit invested. Then it follows that :


at date 1, an amount $1-I$ is available, and the demand will be $\pi_1C_1$, so this yields : $\pi_1C_1 = 1-I$
at date 2, an amount $RI$ is available, and the demand will be $\pi_2C_2$, so this yields : $\pi_2C_2 = RI$