The difference between convergence in probability and convergence in distribution. I'm confused with the concepts of convergence in probability and convergence in distribution. After reading some examples in Wiki, can I say convergence in probability means the decrease of variance as n goes to infinity, that is we become more and more confident that one outcome in the sample space will happen? Convergence in distribution just indicates the probability distribution.

One of the key differences is that convergence in probability tells you something about random variables being close in a pointwise sense (with a high probability) whereas convergence in distribution says only something about the closeness of the distributions. 
Let me illustrate this with an example: Take to identically distributed random variables $X$ and $Y$ and define $$X_n := Y \qquad \text{for all $n \geq 1$}.$$ Since all the random variables have the same distribution, we clearly have $X_n \to X$ in distribution. On the other hand, we can, in general not, expect that $X$ is close to $Y$ in a pointwise sense. For instance, if $X \sim N(0,1)$ and we set $Y=X_n:=-X$, then $$\mathbb{P}(|X-X_n|>\delta) = \mathbb{P}(|X|>\delta/2)>0$$ which means that $X_n$ does not convergence in probability to $X$.
Convergence in distribution does not even require that the random variables are all defined on the same probability space, i.e. each random variable $X_n$ may be defined on some probability space $(\Omega_n,\mathcal{A}_n,\mathbb{P}_n)$. In particular, it doesn't even make sense to ask whether the random variables $X_n$ are being close to each other since we can't calculate the probability of the set
$$\{\omega \in ??; |X_n(\omega)-X_m(\omega)| >\delta\}$$
(probability with respect to which measure? $\mathbb{P}_n$ or $\mathbb{P}_m$...? In fact, we can't even write down the set properly since the $\omega$'s are elements in different probability spaces.)
