Lmer Random Effects Interpretation

Sorry, I am new to linear mixed models. I run a linear mixed model and get the following Output:

Formula: all_data$$ss_item_1 ~ all_data$$sub_means1 + (1 | session) + (1 |
Code)

Random effects:

Groups   Name        ..........Variance..Std.Dev.

session  (Intercept)  ..0.09047  0.3008
Code     (Intercept) .....0.15016  0.3875
Residual           .................  0.79609  0.8922

Number of obs: 299, groups:  session, 50; Code, 30

Fixed effects:
.............Estimate Std. Error       df t value     Pr(>|t|)
(Intercept)         ................. 1.49763    0.21252 24.72077   7.047 0.0000002333

all_data$sub_means1 0.78926 0.09197 23.34523 8.582 0.0000000112 Correlation of Fixed Effects: (Intr) all_dt$sb_1 -0.875


My question is, what exactly does the Residuals Variance of the random effects tells me (the 0.79609)? I see that my fixed effect predicts the criterion significantly but I want to report about the random effects too. I just don't understand it correctly.

With icc_specs(model0) %>% mutate_if(is.numeric, round, 5) I explored the following table. percent adds up to 1 but still I do not know 1 of what.

grp ..........vcov...... icc..... percent

session .....0.09047 0.08726... 8.72638

Code .....0.15016.... 0.14484....... 14.48406
Residual .....0.79609 0.76790 ...76.78955

Thank you very much in advance.

However, the way I think about the random structure is this: The model has 3 sources of randomness - randomness due to the grouping variable session, randomness due to the grouping variable Code, and then whatever is left (residual variance).
In terms of your code, I don't know what icc_specs does specifically, but I expect all it does is apportion the variance to each grouping variable, so that the total adds up to 1 and each grouping variable (plus the residual) variance will get it's own proportion of it. Usually these calculations are based on variance, not standard deviation.