Heterozygosity under genetic drift
The notation at this site resembles that in your question but preserves the $\frac{x_t}{2N}$ notation for probability of selecting an allele. 

$$E[\frac{x_{t+1}}{2N})(1 - \frac{x_{t+1}}{2N} )|x_t] = (\frac{x_{t}}{2N})(1 - \frac{x_{t}}{2N}) (1 - \frac{1}{2N})  $$

The expression $(\frac{x_{t}}{2N})(1 - \frac{x_{t}}{2N}) $ is the probability of heterozygosity at step $t.$ 

Your expression says that the expected heterozygosity at step $(t+1)$ is equal to the heterozygosity at step at $t$ multiplied by $(1-\frac{1}{2N}).$

For a population of size $2N,~(1-\frac{1}{2N})^{2N}\approx 1/e,$ so large populations are insulated from this effect and small ones may lose genetic diversity rapidly. 

A typical explanation can be found here. The notation at this site condenses the expression $(\frac{x_{t}}{2N})(1 - \frac{x_{t}}{2N}) $ to $H_n$ and explicitly says it is $1 - F_n, $ in which $F_n$ is the probability of homozygous at step $n.$