is there any difference between taking more samples and a sample with more observations? I'm quite confused with the difference between taking the average of more samples and taking the average of a sample with more observations.  Do you get unbiased estimates by taking more sample of more observations?
 A: Suppose you take 10 samples of 50 and your friend takes one sample of 500. There is no difference in the amount of information you can extract versus your friend. In theory you are both under the same conditions because you have the same amount of data. Problems could arise if samples are not independent, but under independent random sampling you and your friend are dealing with equivalent situations.  
Let's look at the variance. Suppose you average your 10 sample means. So you have $$\bar x_{samples}=(1/10)(\bar x_1+\bar x_2 + \cdots + \bar x_{10}) $$ 
The variance of this random  variable is  $(1/10^2)*(10)*(\sigma^2/50)= \sigma^2/500,$ where $\sigma^2$ is the population variance. 
But this is the same as the variance of the random variable $$\bar x_{500}=(1/500)*(x_1 + x_2 + \cdots + x_{500}),$$ which your friend uses. 
To answer your question about bias, both estimators are unbiased for the population mean. That is, the expected values of both are equal to the population mean. 
A: In some areas (e.g. analytical chemistry) the term sample means  a piece (or quantity) of material that is to be analyzed (specimen). From a statistical point of view, you then have a nested/clustered/hierarchical structure of your sampling and the assumption of "independent random sampling" in @soakley's answer is not met: 
multiple observations of the same specimen are often more similar than multiple observations from different specimen (aka samples).
That is, $\sigma^2_\text{within specimen} < \sigma^2_\text{between specimen}$.
E.g. for chemical analyses of an ore, a sampling error $\sigma^2_\text{between specimen}$ that is $\leq 3 \times $ the analysis error $\sigma^2_\text{within specimen}$ would be considered typical (properly done sampling). 
If your sampling is done properly (for both physical and statistical meaning of "sample"), then taking 50 or 500 specimen/samples both yield unbiased estimates of the target property. If it is not done properly, then both can be biased. Whether the estimate is biased or not does not depend on the number of specimen / (statistical) sample size, but on the sampling procedure.      
But if $\sigma^2_\text{within samples/specimen} < \sigma^2_\text{between samples/specimen}$, the uncertainty (standard error) after 50 samples/ specimen $\times$ 10 observations each is larger than the uncertainty after 500 samples/ specimen $\times$ 1 observation each. 
If only 1 specimen is analyzed with 500 observations, then the estimate is still unbiased, but unfortunately you have no idea of the sampling error $\sigma^2_\text{between samples/specimen}$ other than that you can assume that it is a multiple (e.g. an order of magnitude higher) than the variance $\sigma^2_\text{within samples/specimen}$ you observe between your 500 observations. 
