How to interpret parameter estimates in factor prediction ( in R ) So I have some data set in a .cs

In R, the lm() function is very useful to perform a regression analysis on categorical variables. To understand how R manages the data with this command, we can remind that, if we have m factors, each with n observations, R starts from the basic equation of the classical random effects model
$Y_{ij}=\mu +U_i+{\mathrm{ϵ<!--\; ϵ\; -->}}_{ij}$
where $Y_{ij}$ is the value of the $j^{th}$ item of the $i^{th}$ factor, $\mathrm{\mu <!--\; \mu \; -->}$ is the average score for the whole population, $U_i$ is the factor-specific random effect, and ${\mathrm{ϵ<!--\; ϵ\; -->}}_{ij}$ is the individual-specific effect. To make an example, let us suppose that m soccer teams are randomly chosen among all teams of the world, and that n players are randomly chosen from each selected team. The performance scores for each player in a given year are collected. Applying the random effect model, $Y_{ij}$ is the score of the $j^{th}$ player of the $i^{th}$ team, $\mathrm{\mu <!--\; \mu \; -->}$ is the average random score for the entire population, $U_i$ is the random team-specific effect, and ${\mathrm{ϵ<!--\; ϵ\; -->}}_{ij}$ is the player-specific effect. In this model, the term $U_i$ quantifies the difference between the average score of the team i and the overall average score observed in the entire population. It is defined as a "random" effect because each team have been randomly selected from a larger number of teams. In your case, these considerations can be directly applied to your three factors/levels, each with 15 observations.
However, you have to consider that the lm() function of R typically uses a reparameterization , commonly called the "reference cell model". Here, one of the $U_i$ (usually the first) is set to zero and is used as a reference. In this approach, which we could be write as
$Y_{ij}={\mu }^{\ast <!--\; \ast \; -->}+U_i+{\mathrm{ϵ<!--\; ϵ\; -->}}_{ij}$
the mean of category 1 is taken as the intercept ${\mathrm{\mu <!--\; \mu \; -->}}^{\ast <!--\; \ast \; -->}$, and the term Ui measures the difference between the average score of the team i and the average score observed in the reference category 1. So, looking at the R output in your question, the intercept corresponds to ${\mathrm{\mu <!--\; \mu \; -->}}^{\ast <!--\; \ast \; -->}$ (the mean of the first level), the coefficient $x_2$ is an estimate of the difference in means between level 2 and level 1, and similarly the coefficient $x_3$ is an estimate of the difference in means between level 3 and level 1. Note that the output does not include any $x_1$ coefficient, just because the first level is the reference. Also note that in your output $x_2$ is rather small and $x_3$ is large; accordingly, the t value is large for $x_3$ and small for $x_2$. This means that the difference between level 3 and the reference level 1 is probably highly significant, whereas that between level 2 and the reference level 1 is probably not significant (however, to correctly assess significance, you have to look at the p values, which are given in the R output). The high t value of the intercept simply expresses the significance for testing the difference between the mean of the first category and 0, and therefore is not particularly useful.