I have used once the bootstrap sampling method to obtain a confidence interval for the expected daily returns that I had calculated using some data given.
As far as I have understood, this method can be used even when the distribution of the random variable, in this case of the expected value of the daily returns, hasn't a "nice" distribution, but I would like to have a precise explanation of when should this method be used and why.
Should for example the sample, in my case it was the daily returns, be Gaussian (or normally) distributed? My intuition is of course to say no, but again, a precise explanation would be more helpful.
In general, when is the bootstrap sampling method not applicable? And when is it applicable?
I believe you are thinking of a 'nonparametric bootstrap'. In practice, it works for data from almost all distributions. The fundamental idea is that the empirical cumulative distribution function of the sample is used as a substitute for the cumulative distribution function of the population.
If the data are binary (say, values 0 and 1), then a binomial test is more useful than a bootstrap. If the data are substantially skewed (not essentially symmetrical) then certain 'naive' bootstrap procedures need bias correction to give a useful confidence interval for the population mean. The actual coverage probability of a 95% CI based on a small sample may be a little less than 95%.
If you have a very large sample (maybe over 100 observations), then it is probably OK to use a standard one-sample t test even if the data are not exactly normal. You might compare results from the bootstrap and t procedures. If they are substantially the same for practical purposes, then fine. If not, maybe you can try to understand the reason for the discrepancy. (Extreme skewness, lots of straggling far outliers in one or both tails, marked bimodality, and so on.)
Recently, I posted an example of a nonparametric bootstrap using the 'quantile method'. That should work for the type of data you describe. See question 1577585.
If you want to describe and show your data and the CI resulting from such a procedure, please edit these into your Problem as an 'addendum', and leave me a note beneath this Answer. I will have a look at it.