How Variance becomes infinite The text is from Introduction to statistical learning,  by James et al.,  page 203-204 The doubts are highlighted in bold. Please help me to understand this.
p-No. of Independent variables , n-No.of obs.

If $p>n$, then there is no longer a unique least squares coefficient estimate: the variance is inﬁnite so the method cannot be used at all.

(How does variance become infinite?) 

By constraining or shrinking the estimated coefficients, we can often substantially reduce the variance at the cost of a negligible increase in bias.  

(What does constraining or shrinking the estimated coefficients mean?)

This can lead to substantial improvements in the accuracy with which we can predict the response for observations not used in model training. 

(How?)
 A: Concerning the infinite variance of the least-squares estimator for the regression coefficients in case $p>n$, the book is right, in the following sense. If $p\leqslant n$ and the true model of the data is the one you are considering, i.e.
$$
Y_i = \beta_0 + \beta_1 x_{1i} + \ldots + \beta_{p-1} x_{p-1,i} + \varepsilon_i
$$
for $i=1,\ldots,n$ and all $\varepsilon_i$ are independent and normally distributed with mean zero and variance $\sigma^2$, then it can be shown that the column vector of least-squares estimates for $\beta_j$ ($j=0,\ldots,p-1$) has a multivariate normal distribution. That is, 
$$
  \hat{\boldsymbol{\beta}} \sim \text{N}(\boldsymbol{\beta}, \sigma^2(\boldsymbol{x}'\boldsymbol{x})^{-1})
$$
with $\boldsymbol{\beta}=\left[\matrix{\beta_0\\ \beta_1\\ \vdots \\ \beta_{p-1}}\right]$, $\hat{\boldsymbol{\beta}}=\left[\matrix{\hat{\beta_0}\\ \hat{\beta_1}\\ \vdots \\ \hat{\beta_{p-1}}}\right]$ and the design matrix $\boldsymbol{x} = \left[\matrix{1 & x_{11} & \cdots & x_{p-1,1}\\ \vdots & \vdots & & \vdots\\ 1 & x_{n1} & \cdots & x_{p-1,n}}\right]$.
So the coefficient estimates have the true coefficients as their mean, which is good news because that makes these estimates $\hat{\boldsymbol{\beta}}$ unbiased. 
However, the main point here is that the Gram matrix $\boldsymbol{x}'\boldsymbol{x}$ is not always invertible, in which case its inverse does not exist, or, as the book says "is infinite". That is just like the number $1/0$ is "infinite" or does not exist. In that situation, the estimates $\hat{\boldsymbol{\beta}}$ are not unique, there are many values which minimise the sum of squares of the residuals. 
If $p>n$ the columns of the design matrix $\boldsymbol{x}$ necessarily become linearly dependent and the Gram matrix $\boldsymbol{x}'\boldsymbol{x}$ will not have full rank. That means its inverse does not exist (or is infinite), and neither does the variance of $\hat{\boldsymbol{\beta}}$.
