Why does your title say partial correlation table? The output doesn't say that. It seems like a correlations table. Correlation is a measure of how do two variables move together 'linearly' i.e. if x increases then so does y or may be y increases in opposite direction. The correlation of the variable with itself is always 1. So 1(intention to quit) has a value of 1 against itself & similarly you can see 1 in 2-2,3-3 & so on. For 2-1 you see a value of 0.020 i.e. correlation between # of skills & intention to quit is 0.02 or 2% which is a weak but positive correlation. The correlation between 3 & 1 is -ve which means that they move in opposite direction. A star against a number indicates that the correlation is statistically significant that means there is less than 1% chance that correlation will be equal to 0.

These variables as you see are correlated among each other. So while measuring relationship between two variables the correlation gets influenced by other variables. If you measure the correlation after removing the influence/effect of other variables then it is called partial correlation (which I suspect is not given in this table). For example 5 & 8 have a strong correlation (47%) & so do 6 & 8(45%). Therefore, the correlation between 5&6 will be heavily influenced by 8. The partial correlation between 5 & 6 would be measured after removing effect of 8 from both 5 & 6.

Hope it helps.