Please explain to me the difference in Bayesian estimate and Maximum likelihood estimate?
It is a very broad question and my answer here only begins to scratch the surface a bit. I will use the Bayes's rule to explain the concepts. 

Let’s assume that a set of probability distribution parameters,  $\theta$, best explains the dataset $D$. We may wish to estimate the parameters $\theta$ with the help of the Bayes’ Rule:

$$p(\theta|D)=\frac{p(D|\theta) * p(\theta)}{p(D)}$$

$$posterior = \frac{likelihood * prior}{evidence}$$

The explanations follow:

Maximum Likelihood Estimate

With MLE,we seek a point value for $\theta$ which maximizes the likelihood, $p(D|\theta)$, shown in the equation(s) above. We can denote this value as $\hat{\theta}$. In MLE, $\hat{\theta}$ is a point estimate, not a random variable.

In other words, in the equation above, MLE treats the term $\frac{p(\theta)}{p(D)}$ as a constant and does NOT allow us to inject our prior beliefs, $p(\theta)$, about the likely values for $\theta$ in the estimation calculations.

Bayesian Estimate

Bayesian estimation, by contrast, fully calculates (or at times approximates) the posterior distribution $p(\theta|D)$. Bayesian inference treats $\theta$ as a random variable. In Bayesian estimation, we put in probability density functions and get out probability density functions, rather than a single point as in MLE. 

Of all the $\theta$ values made possible by the output distribution $p(\theta|D)$, it is our job to select a value that we consider best in some sense. For example, we may choose the expected value of $\theta$ assuming its variance is small enough. The variance that we can calculate for the parameter $\theta$ from its posterior distribution allows us to express our confidence in any specific value we may use as an estimate. If the variance is too large, we may declare that there does not exist a good estimate for $\theta$.

As a trade-off, Bayesian estimation is made complex by the fact that we now have to deal with the denominator in the Bayes' rule, i.e. $evidence$. Here evidence -or probability of evidence- is represented by:

$$p(D) = \int_{\theta} p(D|\theta) * p(\theta) d\theta$$

This leads to the concept of 'conjugate priors' in Bayesian estimation. For a given likelihood function, if we have a choice regarding how we express our prior beliefs, we must use that form which allows us to carry out the integration shown above. The idea of conjugate priors and how they are practically implemented are explained quite well in this post by COOlSerdash.
