Can someone please explain what this regression model means? I'm studying the link between a regime's violation of its citizens' physical integrity rights and civil conflict. There are 4 independent variables (political imprisonment, torture, disappearances and killings) and one dependent variable (civil conflict). So I ran a regression formula using all of the variables and the results are below, but I don't know how to actually read them. 

 A: The R-squared is telling you that of all the variability in the dependent variable, only 38% is explained by the independent variables in the linear model you propose. This may not be that bad giving that you are not trying to make predictions based on the linear equation that @RustyStatistician formulated for you.
The second thing to notice is that the relationship between "civil conflict" and both "killings" and "disappearances" is statistically significant at a $p$ value of $<1\%$. You can't say the same of "political imprisonment" and "torture."
The negative sign for both significant regressors is surprising in that it indicates that there is a negative relationship between disappearances and killings, and the dependent variable (civil conflict). The labels in plain English seem to point to a positive correlation, where an increase in disappearances and killings would lead to more civil conflict, not less. But it's reason to review how these variables are measured and coded.
As noted in other comments, it is also important to question whether an OLS regression is the best model. For instance, if the dependent variable is measured in counts, a Poisson model may be more appropriate.
As an aside, please be aware of the rich semiotic depth in the name of the RHS (right-hand side) variables and LHS (left-hand side) of the OLS regression equation as beautifully captured in this Wikipedia entry, and transcribed below (if it seems tangential you can safely ignore this last part):

An independent variable is also known as a "predictor variable", "regressor", "controlled variable", "manipulated variable", "explanatory variable", "exposure variable" (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or an "input variable.
A dependent variable is also known as a "response variable", "regressand", "predicated variable", "measured variable", "explained variable", "experimental variable", "responding variable", "outcome variable", and "output variable".

A: So you basically ran a linear regression in Stata and the output that you have above is telling you that you obtained the following fitted model:
$$\text{internal}=.063-0.175\times\text{PolPris}+.0348\times\text{Torture}-0.205\times\text{Dissap}-0.134\times\text{Kill}$$
Likewise, the P>|t| column gives you the p-values associated with each explanatory variables estimated coefficient, and the next two columns give the associated 95% confidence intervals for the coefficients as well. 
However, there isn't much more anyone can tell you about this problem until you give us more information about what all the variables mean. I am also curious to know are all of the variables continuous or some binary or multi-categorical?
Without knowing much more about the problem you are working on we really can't say much more about the interpretation on a meaningful level.
