I have run my analysis and having had the correlation coefficient, accepted the null hypothesis only when the Significance >0.5 and looking for coefficient values above 0.6.

I assume you mean

*rejected* rather than accepted the null hypothesis? There is no way to provide evidence to accept the null hypothesis in the conventional null hypothesis testing strategy. Is there any particular reason why you have chosen 0.5/0.6 as cutoff values? In terms of deciding whether there is evidence to reject a null hypothesis one would usually use a p value with a cutoff of 0.1, 0.05 or 0.01, not the coefficient itself. 0.5 is, however, a commonly used cutoff for a "large" correlation, as per

Jacob Cohen's (1988) guidelines for correlation magnitude.

Now, how do I translate this number in the practical world?

0.6*0.6= 36% of sharing variance.

This is what I know but unfortunately this is not enough as I need to know

•How is it possible to translate it in practical figures? What does it exctly mean in terms of my sample and my population?

This is always a difficult question in statistics! Practical significance of results is always something that takes a lot of thought, integration with existing theory and evidence, and often subjective interpretation. Cohen's guidelines for interpreting magnitude can be useful, as mentioned before: 0.1-0.3 = small, 0.3-0.5 = moderate, 0.5+ = strong.

•Why there is no correlation between products that are often bought in combination?

You might need to look into the individual examples of this more carefully to work this out - it will depend on how frequently "often" means, and what the customers who aren't buying them in combination are doing. Do be careful, though, not to interpret a correlation under your cutoff of 0.5 or that is statistically insignificant as "no" correlation. A statistically insignificant relationship does not mean no relationship.