Can anyone explain the difference between observed variables and unobserved variables (preferably in plain English ) ?
Observed variables are variables for which you have measurements in your dataset, whereas unobserved (or latent) variables are variables for which you don't.
When your analysis reveals correlations between observed variables, you might look for unobserved variables to explain the correlation, especially in cases where you doubt that there's a direct causal relationship between them. To offer a contrived example, suppose your dataset includes strongly correlated variables "ice cream consumption" and "air conditioner usage". You might suspect that there's an unobserved variable (temperature), acting as a common cause, driving the correlation.
Sometimes the unobserved variable is unobserved because it isn't directly measurable. (Perhaps the variable is more theoretical in nature, or perhaps the variable is in principle directly measurable, but it would be difficult/expensive to measure it in practice.) For example, we can't measure intelligence directly, so we use proxy measurements such as performance on intelligence tests as a substitute.
Are you doing research within economics? Usually, the unobservable characteristics are those that are captured by the error term and bias your estimates, for instance through heteroskedasticity. Let's me give you an example.
When you conduct a so called correspondence test in the labor market to study ethnic discrimination in hiring, you send out bogus matched job applications. One application concerns the "red" applicant while the other application concerns the "green" applicant (where "green" and "red" are two whatever ethnic groups). The ethnicity is the only observable characteristic that differ between the two bogus applicants; however, in the applications there are many other characteristics that are the same (well, actually they are equivalent, not really the same) for the two applicants, such as: reached level of studies, age, work experience, etc... All these characteristics are observable (from the point of view of the experimenter and from that of the employer) because they are listed in the CV, while the ethnicity can be understood from the applicants' name.
Other characteristics that are not listed in the CV are thus observable neither by the employers nor by the experimenters. These characteristics are the so called "unobservable characteristics". These unobservable characteristics will affect the estimate of discrimination in hiring through heteroskedasticity (=different variance of the residuals, for the two compared groups). For more insights on this point see this article and this article.
A similar problem arises from audit tests where, instead of sending fictitious written applicants, the experimenter sends two actors to apply in person to job interview. The two actors are matched on all characteristics except for the ethnic group. However, there will be different characteristics between the two applicants that have not been observed by the experimenter, but that will be observed by the employer, also in this case we speak of unobservable characteristics. For instance, one applicant has a more pleasant voice, or applicant stinks a little during the day of the interview or did not comb his/her hair properly, etc...while these examples may sound silly, these different unobservable characteristics might eventually determine a systematic difference in the hiring decisions for the two bogus applicants and thus bias the results.