What does it mean that the hypothesis space does not contain the target concept? I read that the algorithm candidate elimination would not converge if the Hypothesis space $H$ does not contain the target concept.

You can look it up here.
I quoted from the 5th heading:

The version space learned by the Candidate elimination algorithm will converge toward the hypothesis that correctly describes the target concept, provided


(1) there are no errors in the training examples, and


(2) there is some hypothesis in H that correctly describes the target concept.


What does this and and what would be a concrete example for a hypothesis space that does not contain the target concept?
I am puzzled because I thought the hypothesis space would be the set of all possible hypothesis, then why should it not contain a specific hypothesis for the target concept?
 A: I don't know anything about 'candidate elimination', but I'll attempt an answer.
The key idea is that statistical methods all work within a statistical model. That model is a collection of assumptions and relationships (usually formulae), and the admissible hypotheses are not "all possible hypotheses", but all of the hypotheses that are contained within the model. In most cases (maybe all) the things that we call hypotheses are better described as parameter values within the space of the statistical model. Those parameter values can be vectors of multiple parameters (e.g. population mean and standard deviation together for Student's t-test) or they may be just the parameter of interest with the other parameters being dealt with in a variety of ways.
If the candidate hypothesis of interest (or perhaps it is the 'true' candidate hypothesis) is not a point (or vector) within the parameter space of the statistical model then no output of the statistical method can point towards it.
Now, a concrete example in an area with which I am comfortable. Say that I wish to determine the effect of an intervention on the number of virus particles produced per infected cell and I am able to make the relevant measurements. I gather a couple of datasets (control and intervention) and analyse the difference between their means, using a simple Student's t-test to the result to evaluate the strength of the evidence against the null hypothesis that the treatment effect is zero. (I would not omit the direct inspection of the size of the observed effect relative to what would be scientifically meaningful, but that is not part of the statistical evaluation.)
That analysis presents no problem as long as the 'true' hypothesis is contained within the space of mean and standard deviations. But what if the population mean naturally varies over time and that rate is affected by the treatment? Student's t-test would not characterise any evidence relevant to the time-related effect. A different analysis which included information from the time domain (I think that an analysis of variance could be set up in that manner, or a regression analysis) would be needed. And it's worth noting that the nature of the datasets required might be different as well.
The choices of analysis and data gathering strategies will always limit the admissible hypotheses.
